DOI: 10.1007/bf01720068. On the global minimization of concave functions

On the global minimization of concave functions

10.1007/bf01720068

Crossref journal-article

Springer Science and Business Media LLC

Operations-Research-Spektrum (297)

Authors 1

R. Horst (first)

References 51 Referenced 58

Al-Khayyal F, Falk I (1983) Jointly constrained biconvex programming. Math Oper Res 8:273–286 (10.1287/moor.8.2.273) / Math Oper Res by F Al-Khayyal (1983)
Altman M (1968) Bilinear programming. Bull Acad Polon Sci Ser Sci Math Astronom Phys 16:741–746 / Bull Acad Polon Sci Ser Sci Math Astronom Phys by M Altman (1968)
Balas E (1975) Nonconvex quadratic programming problems via generalized polars. SIAM J Appl Math 28:335–349 (10.1137/0128029) / SIAM J Appl Math by E Balas (1975)
Balas E, Burdet CA (1973) Maximizing a convex quadratic function subject to linear constraints. Management Sci. Report No. 299, GSIA, Carnegie-Medon University, Pittsburgh, P / Management Sci. Report No. 299 by E Balas (1973)
Bali S (1973) Minimization of a concave function on a bounded convex polyhedron. PhD Dissertation, University of California, Los Angeles / PhD Dissertation by S Bali (1973)
Ban VT (1982) A finite algorithm for minimizing a concave function under linear constraints and its applications. Preprint, Institute of Mathematics, Hanoi / A finite algorithm for minimizing a concave function under linear constraints and its applications by VT Ban (1982)
Benson H (1984) A finite algorithm for concave minimization over a polyhedron, Paper presented at the TIMS/ORSA meeting. San Francisco 1984
Cabot AV (1974) Variations on a cutting plane method for solving concave minimization problems with linear constraints. Naval Res Logist Qu 21:265–274 (10.1002/nav.3800210206) / Naval Res Logist Qu by AV Cabot (1974)
Cabot AV, Francis RL (1970) Solving certain nonconvex quadratic minimization problems by ranking the extreme points. Oper Res 18:82–86 (10.1287/opre.18.1.82) / Oper Res by AV Cabot (1970)
Carillo MI (1977) A relaxation algorithm for the minimization of a quasiconcave function on a convex polyhedron. Math Programming 13:69–80 (10.1007/BF01584324) / Math Programming by MI Carillo (1977)
Falk I, Hoffmann KL (1976) A successive underestimation method for concave minimization problems. Math Oper Res 1:251–259 (10.1287/moor.1.3.251) / Math Oper Res by I Falk (1976)
Falk I, Hoffmann KL (1982) Concave minimization via collapsing polytopes. Preprint T-438, The George Washington University, Washington, DC / Preprint T-438 by I Falk (1982)
Falk I, Soland RM (1969) An algorithm for separable nonconvex programming problems. Manag Sci 15:550–569 (10.1287/mnsc.15.9.550) / Manag Sci by I Falk (1969)
Gallo G, Ulkucu A (1977) Bilinear programming: an exact algorithm. Math Programming 12:173–194 (10.1007/BF01593787) / Math Programming by G Gallo (1977)
Glover F (1973) Concave programming applied to a special class of 0–1 integer programs. Oper Res 21:135–140 (10.1287/opre.21.1.135) / Oper Res by F Glover (1973)
Gould FJ, Tolle JW (1983) Complementary pivoting on a pseudomanifold structure with applications in the decision scienes. Heldermann, Berlin / Complementary pivoting on a pseudomanifold structure with applications in the decision scienes by FJ Gould (1983)
Hoffmann KL (1975) A successive underestimating method for concave minimization problems. PhD Dissertation, The George Washington University, Washington, DC / PhD Dissertation by KL Hoffmann (1975)
Hoffmann KL (1981) A method for globally minimizing concave functions over convex sets. Math Programming 20:22–32 (10.1007/BF01589330) / Math Programming by KL Hoffmann (1981)
Horst R (1976) Zur Charakterisierung affin-linearer Hüllfunktionale. ZAMM 56:T347-T348 (10.1002/zamm.19765613161) / ZAMM by R Horst (1976)
Horst R (1976) A new branch-and-bound approach for concave minimization problems. Lecture Notes in Computer Sciences 41:330–337 (10.1007/3-540-07623-9_296) / Lecture Notes in Computer Sciences by R Horst (1976)
Horst R (1976) An algorithm for nonconvex programming problems. Math Programming 10:312–321 (10.1007/BF01580678) / Math Programming by R Horst (1976)
Horst R (1979) Nichtlineare Optimierung. Carl Hanser, München / Nichtlineare Optimierung by R Horst (1979)
Horst R (1980) A note on the convergence of an algorithm for nonconvex programming problems. Math Programming 19:237–238 (10.1007/BF01581645) / Math Programming by R Horst (1980)
Horst R (1982) Konkave Minimierungsprobleme in Operations Research. OR-Proceeding 1981:580–591 / OR-Proceeding by R Horst (1982)
Horst R (1984) On the convexification of nonlinear programming problems: An applications-oriented survey. Eur J Oper Res 15:382–392 (10.1016/0377-2217(84)90107-3) / Eur J Oper Res by R Horst (1984)
Jacobsen SE (1981) Convergence of a Tuy-Type-Algorithm for concave minimization subject to linear inequality constraints. Appl Math Optim 7:1–9 (10.1007/BF01442106) / Appl Math Optim by SE Jacobsen (1981)
Kelly JE (1960) The cutting plane method for solving convex programs. SIAM J Appl Math 8:703–712 (10.1137/0108053) / SIAM J Appl Math by JE Kelly (1960)
Koehler G, Whinston AB, Wright GP (1975) Optimization over Leontiev substitution systems. North Holland, Amsterdam / Optimization over Leontiev substitution systems by G Koehler (1975)
Kough PF (1979) The indefinite quadratic programming problem. Oper Res 27:516–533 (10.1287/opre.27.3.516) / Oper Res by PF Kough (1979)
Konno H (1976) A cutting plane algorithm for solving bilinear programs. Math Programming 11:14–27 (10.1007/BF01580367) / Math Programming by H Konno (1976)
Konno H (1976) Maximization of a convex quadratic function subject to linear constraints. Math Programming 11:117–127 (10.1007/BF01580380) / Math Programming by H Konno (1976)
Majthai A, Whinston A (1974) Quasiconcave minimization subject to linear constraints. Discrete Math 9:35–59 (10.1016/0012-365X(74)90070-3) / Discrete Math by A Majthai (1974)
Mangassarian OL (1978) Characterization of linear complementarity problems as linear programs. Math Programming Study 7:74–88 (10.1007/BFb0120783) / Math Programming Study by OL Mangassarian (1978)
Meyer PA (1966) Probabilité et potentiels. Herman, Paris / Probabilité et potentiels by PA Meyer (1966)
Ragavachari M (1969) On connections between zero-one integer programming and concave programming under linear constraints. Oper Res 17:680–684 (10.1287/opre.17.4.680) / Oper Res by M Ragavachari (1969)
Rockafellar RT (1970) Convex Analysis. Princeton University Press, Princeton (10.1515/9781400873173) / Convex Analysis by RT Rockafellar (1970)
Rosen JB (1983) Global minimization of a linearly constrained concave function by partition of the feasible domain. Math Oper Res 8:215–230 (10.1287/moor.8.2.215) / Math Oper Res by JB Rosen (1983)
Sheraly HD, Shetty CM (1980) A finitely convergent algorithm for bilinear programming problems using polar cuts and disjunctive face cuts. Math Programming 19:14–31 (10.1007/BF01581626) / Math Programming by HD Sheraly (1980)
Taha H (1973) Concave minimization over a convex polyhedron. Naval Res Logist Qu 20:533–548 (10.1002/nav.3800200313) / Naval Res Logist Qu by H Taha (1973)
Thieu TV (1978) Relationship between bilinear programming and concave minimization under linear constraints. Acta Math Vietnamica 5:106–113 / Acta Math Vietnamica by TV Thieu (1978)
Thoai NV, Tuy H (1980) Convergent algorithms for minimizing a concave function. Math Oper Res 5:556–566 (10.1287/moor.5.4.556) / Math Oper Res by NV Thoai (1980)
Tuy H (1964) Concave programming under linear constraints. Dokl Adad Nauk SSSR 159:32–35 (Translated (1964): Soviet Math 5:1437-1440) / Dokl Adad Nauk SSSR by H Tuy (1964)
Tuy H (1982) Global maximization of a convex function over a closed, convex, not necessarily bounded set. Cahiers de Mathématiques de la Décision No 8223, Université Paris-Dauphine
Tuy H (1983) Global minimization of a difference of two convex functions. Preprint, Institute of Mathematics, Hanoi / Global minimization of a difference of two convex functions by H Tuy (1983)
Tuy H (1983) On outer approximation methods for solving concave minimization problems. Report Nr. 108, Forschungsschwerpunkt Dynamische Systeme, Universität Bremen
Veinott AF (1967) The supporting hyperplane method for unimodal programming. Oper Res 15:147–152 (10.1287/opre.15.1.147) / Oper Res by AF Veinott (1967)
Veinott AF (1969) Minimum concave-cost solution of Leontief substitution models of multi-facility inventory systems. Oper Res 17:262–291 (10.1287/opre.17.2.262) / Oper Res by AF Veinott (1969)
Zangwill WI (1966) A deterministic multi-product multifacility production and inventory model. Oper Res 14: 486–507 (10.1287/opre.14.3.486) / Oper Res by WI Zangwill (1966)
Zhang XS, Rosen JB (1983) Global concave minimization. Discussion paper, Computer Science development, University of Minnesota
Zwart PB (1973) Nonlinear programming: counterexamples to two global optimization algorithms. Oper Res 21:1260–1266 (10.1287/opre.21.6.1260) / Oper Res by PB Zwart (1973)
Zwart PB (1974) Global maximization of a convex function with linear inequality constraints. Oper Res 22:602–609 (10.1287/opre.22.3.602) / Oper Res by PB Zwart (1974)

Dates

Type	When
Created	20 years, 2 months ago (June 12, 2005, 4:45 a.m.)
Deposited	5 years, 4 months ago (April 7, 2020, 1:42 p.m.)
Indexed	1 month ago (July 28, 2025, 2:31 a.m.)
Issued	40 years, 9 months ago (Dec. 1, 1984)
Published	40 years, 9 months ago (Dec. 1, 1984)
Published Online	40 years, 9 months ago (Dec. 1, 1984)
Published Print	40 years, 9 months ago (Dec. 1, 1984)

Funders 0

None

BibTeX

@article{Horst_1984, title={On the global minimization of concave functions: Introduction and survey}, volume={6}, ISSN={1436-6304}, url={http://dx.doi.org/10.1007/bf01720068}, DOI={10.1007/bf01720068}, number={4}, journal={Operations-Research-Spektrum}, publisher={Springer Science and Business Media LLC}, author={Horst, R.}, year={1984}, month=dec, pages={195–205} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        7,
        28
      ]
    ],
    "date-time": "2025-07-28T06:31:19Z",
    "timestamp": 1753684279460
  },
  "reference-count": 51,
  "publisher": "Springer Science and Business Media LLC",
  "issue": "4",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1984,
            12,
            1
          ]
        ],
        "date-time": "1984-12-01T00:00:00Z",
        "timestamp": 470707200000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "http://www.springer.com/tdm"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1984,
        12
      ]
    ]
  },
  "DOI": "10.1007/bf01720068",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        6,
        12
      ]
    ],
    "date-time": "2005-06-12T08:45:21Z",
    "timestamp": 1118565921000
  },
  "page": "195-205",
  "source": "Crossref",
  "is-referenced-by-count": 58,
  "title": "On the global minimization of concave functions",
  "prefix": "10.1007",
  "volume": "6",
  "author": [
    {
      "given": "R.",
      "family": "Horst",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "297",
  "published-online": {
    "date-parts": [
      [
        1984,
        12,
        1
      ]
    ]
  },
  "reference": [
    {
      "key": "BF01720068_CR1",
      "doi-asserted-by": "publisher",
      "first-page": "273",
      "DOI": "10.1287/moor.8.2.273",
      "volume": "8",
      "author": "F Al-Khayyal",
      "year": "1983",
      "unstructured": "Al-Khayyal F, Falk I (1983) Jointly constrained biconvex programming. Math Oper Res 8:273\u2013286",
      "journal-title": "Math Oper Res"
    },
    {
      "key": "BF01720068_CR2",
      "first-page": "741",
      "volume": "16",
      "author": "M Altman",
      "year": "1968",
      "unstructured": "Altman M (1968) Bilinear programming. Bull Acad Polon Sci Ser Sci Math Astronom Phys 16:741\u2013746",
      "journal-title": "Bull Acad Polon Sci Ser Sci Math Astronom Phys"
    },
    {
      "key": "BF01720068_CR3",
      "doi-asserted-by": "publisher",
      "first-page": "335",
      "DOI": "10.1137/0128029",
      "volume": "28",
      "author": "E Balas",
      "year": "1975",
      "unstructured": "Balas E (1975) Nonconvex quadratic programming problems via generalized polars. SIAM J Appl Math 28:335\u2013349",
      "journal-title": "SIAM J Appl Math"
    },
    {
      "key": "BF01720068_CR4",
      "volume-title": "Management Sci. Report No. 299",
      "author": "E Balas",
      "year": "1973",
      "unstructured": "Balas E, Burdet CA (1973) Maximizing a convex quadratic function subject to linear constraints. Management Sci. Report No. 299, GSIA, Carnegie-Medon University, Pittsburgh, P"
    },
    {
      "key": "BF01720068_CR5",
      "volume-title": "PhD Dissertation",
      "author": "S Bali",
      "year": "1973",
      "unstructured": "Bali S (1973) Minimization of a concave function on a bounded convex polyhedron. PhD Dissertation, University of California, Los Angeles"
    },
    {
      "key": "BF01720068_CR6",
      "volume-title": "A finite algorithm for minimizing a concave function under linear constraints and its applications",
      "author": "VT Ban",
      "year": "1982",
      "unstructured": "Ban VT (1982) A finite algorithm for minimizing a concave function under linear constraints and its applications. Preprint, Institute of Mathematics, Hanoi"
    },
    {
      "key": "BF01720068_CR7",
      "unstructured": "Benson H (1984) A finite algorithm for concave minimization over a polyhedron, Paper presented at the TIMS/ORSA meeting. San Francisco 1984"
    },
    {
      "key": "BF01720068_CR8",
      "doi-asserted-by": "publisher",
      "first-page": "265",
      "DOI": "10.1002/nav.3800210206",
      "volume": "21",
      "author": "AV Cabot",
      "year": "1974",
      "unstructured": "Cabot AV (1974) Variations on a cutting plane method for solving concave minimization problems with linear constraints. Naval Res Logist Qu 21:265\u2013274",
      "journal-title": "Naval Res Logist Qu"
    },
    {
      "key": "BF01720068_CR9",
      "doi-asserted-by": "publisher",
      "first-page": "82",
      "DOI": "10.1287/opre.18.1.82",
      "volume": "18",
      "author": "AV Cabot",
      "year": "1970",
      "unstructured": "Cabot AV, Francis RL (1970) Solving certain nonconvex quadratic minimization problems by ranking the extreme points. Oper Res 18:82\u201386",
      "journal-title": "Oper Res"
    },
    {
      "key": "BF01720068_CR10",
      "doi-asserted-by": "publisher",
      "first-page": "69",
      "DOI": "10.1007/BF01584324",
      "volume": "13",
      "author": "MI Carillo",
      "year": "1977",
      "unstructured": "Carillo MI (1977) A relaxation algorithm for the minimization of a quasiconcave function on a convex polyhedron. Math Programming 13:69\u201380",
      "journal-title": "Math Programming"
    },
    {
      "key": "BF01720068_CR11",
      "doi-asserted-by": "publisher",
      "first-page": "251",
      "DOI": "10.1287/moor.1.3.251",
      "volume": "1",
      "author": "I Falk",
      "year": "1976",
      "unstructured": "Falk I, Hoffmann KL (1976) A successive underestimation method for concave minimization problems. Math Oper Res 1:251\u2013259",
      "journal-title": "Math Oper Res"
    },
    {
      "key": "BF01720068_CR12",
      "volume-title": "Preprint T-438",
      "author": "I Falk",
      "year": "1982",
      "unstructured": "Falk I, Hoffmann KL (1982) Concave minimization via collapsing polytopes. Preprint T-438, The George Washington University, Washington, DC"
    },
    {
      "key": "BF01720068_CR13",
      "doi-asserted-by": "publisher",
      "first-page": "550",
      "DOI": "10.1287/mnsc.15.9.550",
      "volume": "15",
      "author": "I Falk",
      "year": "1969",
      "unstructured": "Falk I, Soland RM (1969) An algorithm for separable nonconvex programming problems. Manag Sci 15:550\u2013569",
      "journal-title": "Manag Sci"
    },
    {
      "key": "BF01720068_CR14",
      "doi-asserted-by": "publisher",
      "first-page": "173",
      "DOI": "10.1007/BF01593787",
      "volume": "12",
      "author": "G Gallo",
      "year": "1977",
      "unstructured": "Gallo G, Ulkucu A (1977) Bilinear programming: an exact algorithm. Math Programming 12:173\u2013194",
      "journal-title": "Math Programming"
    },
    {
      "key": "BF01720068_CR15",
      "doi-asserted-by": "publisher",
      "first-page": "135",
      "DOI": "10.1287/opre.21.1.135",
      "volume": "21",
      "author": "F Glover",
      "year": "1973",
      "unstructured": "Glover F (1973) Concave programming applied to a special class of 0\u20131 integer programs. Oper Res 21:135\u2013140",
      "journal-title": "Oper Res"
    },
    {
      "key": "BF01720068_CR16",
      "volume-title": "Complementary pivoting on a pseudomanifold structure with applications in the decision scienes",
      "author": "FJ Gould",
      "year": "1983",
      "unstructured": "Gould FJ, Tolle JW (1983) Complementary pivoting on a pseudomanifold structure with applications in the decision scienes. Heldermann, Berlin"
    },
    {
      "key": "BF01720068_CR17",
      "volume-title": "PhD Dissertation",
      "author": "KL Hoffmann",
      "year": "1975",
      "unstructured": "Hoffmann KL (1975) A successive underestimating method for concave minimization problems. PhD Dissertation, The George Washington University, Washington, DC"
    },
    {
      "key": "BF01720068_CR18",
      "doi-asserted-by": "publisher",
      "first-page": "22",
      "DOI": "10.1007/BF01589330",
      "volume": "20",
      "author": "KL Hoffmann",
      "year": "1981",
      "unstructured": "Hoffmann KL (1981) A method for globally minimizing concave functions over convex sets. Math Programming 20:22\u201332",
      "journal-title": "Math Programming"
    },
    {
      "key": "BF01720068_CR19",
      "doi-asserted-by": "crossref",
      "first-page": "T347",
      "DOI": "10.1002/zamm.19765613161",
      "volume": "56",
      "author": "R Horst",
      "year": "1976",
      "unstructured": "Horst R (1976) Zur Charakterisierung affin-linearer H\u00fcllfunktionale. ZAMM 56:T347-T348",
      "journal-title": "ZAMM"
    },
    {
      "key": "BF01720068_CR20",
      "doi-asserted-by": "publisher",
      "first-page": "330",
      "DOI": "10.1007/3-540-07623-9_296",
      "volume": "41",
      "author": "R Horst",
      "year": "1976",
      "unstructured": "Horst R (1976) A new branch-and-bound approach for concave minimization problems. Lecture Notes in Computer Sciences 41:330\u2013337",
      "journal-title": "Lecture Notes in Computer Sciences"
    },
    {
      "key": "BF01720068_CR21",
      "doi-asserted-by": "publisher",
      "first-page": "312",
      "DOI": "10.1007/BF01580678",
      "volume": "10",
      "author": "R Horst",
      "year": "1976",
      "unstructured": "Horst R (1976) An algorithm for nonconvex programming problems. Math Programming 10:312\u2013321",
      "journal-title": "Math Programming"
    },
    {
      "key": "BF01720068_CR22",
      "volume-title": "Nichtlineare Optimierung",
      "author": "R Horst",
      "year": "1979",
      "unstructured": "Horst R (1979) Nichtlineare Optimierung. Carl Hanser, M\u00fcnchen"
    },
    {
      "key": "BF01720068_CR23",
      "doi-asserted-by": "publisher",
      "first-page": "237",
      "DOI": "10.1007/BF01581645",
      "volume": "19",
      "author": "R Horst",
      "year": "1980",
      "unstructured": "Horst R (1980) A note on the convergence of an algorithm for nonconvex programming problems. Math Programming 19:237\u2013238",
      "journal-title": "Math Programming"
    },
    {
      "key": "BF01720068_CR24",
      "first-page": "580",
      "volume": "1981",
      "author": "R Horst",
      "year": "1982",
      "unstructured": "Horst R (1982) Konkave Minimierungsprobleme in Operations Research. OR-Proceeding 1981:580\u2013591",
      "journal-title": "OR-Proceeding"
    },
    {
      "key": "BF01720068_CR25",
      "doi-asserted-by": "publisher",
      "first-page": "382",
      "DOI": "10.1016/0377-2217(84)90107-3",
      "volume": "15",
      "author": "R Horst",
      "year": "1984",
      "unstructured": "Horst R (1984) On the convexification of nonlinear programming problems: An applications-oriented survey. Eur J Oper Res 15:382\u2013392",
      "journal-title": "Eur J Oper Res"
    },
    {
      "key": "BF01720068_CR26",
      "doi-asserted-by": "publisher",
      "first-page": "1",
      "DOI": "10.1007/BF01442106",
      "volume": "7",
      "author": "SE Jacobsen",
      "year": "1981",
      "unstructured": "Jacobsen SE (1981) Convergence of a Tuy-Type-Algorithm for concave minimization subject to linear inequality constraints. Appl Math Optim 7:1\u20139",
      "journal-title": "Appl Math Optim"
    },
    {
      "key": "BF01720068_CR27",
      "doi-asserted-by": "publisher",
      "first-page": "703",
      "DOI": "10.1137/0108053",
      "volume": "8",
      "author": "JE Kelly",
      "year": "1960",
      "unstructured": "Kelly JE (1960) The cutting plane method for solving convex programs. SIAM J Appl Math 8:703\u2013712",
      "journal-title": "SIAM J Appl Math"
    },
    {
      "key": "BF01720068_CR28",
      "volume-title": "Optimization over Leontiev substitution systems",
      "author": "G Koehler",
      "year": "1975",
      "unstructured": "Koehler G, Whinston AB, Wright GP (1975) Optimization over Leontiev substitution systems. North Holland, Amsterdam"
    },
    {
      "key": "BF01720068_CR29",
      "doi-asserted-by": "publisher",
      "first-page": "516",
      "DOI": "10.1287/opre.27.3.516",
      "volume": "27",
      "author": "PF Kough",
      "year": "1979",
      "unstructured": "Kough PF (1979) The indefinite quadratic programming problem. Oper Res 27:516\u2013533",
      "journal-title": "Oper Res"
    },
    {
      "key": "BF01720068_CR30",
      "doi-asserted-by": "publisher",
      "first-page": "14",
      "DOI": "10.1007/BF01580367",
      "volume": "11",
      "author": "H Konno",
      "year": "1976",
      "unstructured": "Konno H (1976) A cutting plane algorithm for solving bilinear programs. Math Programming 11:14\u201327",
      "journal-title": "Math Programming"
    },
    {
      "key": "BF01720068_CR31",
      "doi-asserted-by": "publisher",
      "first-page": "117",
      "DOI": "10.1007/BF01580380",
      "volume": "11",
      "author": "H Konno",
      "year": "1976",
      "unstructured": "Konno H (1976) Maximization of a convex quadratic function subject to linear constraints. Math Programming 11:117\u2013127",
      "journal-title": "Math Programming"
    },
    {
      "key": "BF01720068_CR32",
      "doi-asserted-by": "publisher",
      "first-page": "35",
      "DOI": "10.1016/0012-365X(74)90070-3",
      "volume": "9",
      "author": "A Majthai",
      "year": "1974",
      "unstructured": "Majthai A, Whinston A (1974) Quasiconcave minimization subject to linear constraints. Discrete Math 9:35\u201359",
      "journal-title": "Discrete Math"
    },
    {
      "key": "BF01720068_CR33",
      "doi-asserted-by": "publisher",
      "first-page": "74",
      "DOI": "10.1007/BFb0120783",
      "volume": "7",
      "author": "OL Mangassarian",
      "year": "1978",
      "unstructured": "Mangassarian OL (1978) Characterization of linear complementarity problems as linear programs. Math Programming Study 7:74\u201388",
      "journal-title": "Math Programming Study"
    },
    {
      "key": "BF01720068_CR34",
      "volume-title": "Probabilit\u00e9 et potentiels",
      "author": "PA Meyer",
      "year": "1966",
      "unstructured": "Meyer PA (1966) Probabilit\u00e9 et potentiels. Herman, Paris"
    },
    {
      "key": "BF01720068_CR35",
      "doi-asserted-by": "publisher",
      "first-page": "680",
      "DOI": "10.1287/opre.17.4.680",
      "volume": "17",
      "author": "M Ragavachari",
      "year": "1969",
      "unstructured": "Ragavachari M (1969) On connections between zero-one integer programming and concave programming under linear constraints. Oper Res 17:680\u2013684",
      "journal-title": "Oper Res"
    },
    {
      "key": "BF01720068_CR36",
      "doi-asserted-by": "publisher",
      "DOI": "10.1515/9781400873173",
      "volume-title": "Convex Analysis",
      "author": "RT Rockafellar",
      "year": "1970",
      "unstructured": "Rockafellar RT (1970) Convex Analysis. Princeton University Press, Princeton"
    },
    {
      "key": "BF01720068_CR37",
      "doi-asserted-by": "publisher",
      "first-page": "215",
      "DOI": "10.1287/moor.8.2.215",
      "volume": "8",
      "author": "JB Rosen",
      "year": "1983",
      "unstructured": "Rosen JB (1983) Global minimization of a linearly constrained concave function by partition of the feasible domain. Math Oper Res 8:215\u2013230",
      "journal-title": "Math Oper Res"
    },
    {
      "key": "BF01720068_CR38",
      "doi-asserted-by": "publisher",
      "first-page": "14",
      "DOI": "10.1007/BF01581626",
      "volume": "19",
      "author": "HD Sheraly",
      "year": "1980",
      "unstructured": "Sheraly HD, Shetty CM (1980) A finitely convergent algorithm for bilinear programming problems using polar cuts and disjunctive face cuts. Math Programming 19:14\u201331",
      "journal-title": "Math Programming"
    },
    {
      "key": "BF01720068_CR39",
      "doi-asserted-by": "publisher",
      "first-page": "533",
      "DOI": "10.1002/nav.3800200313",
      "volume": "20",
      "author": "H Taha",
      "year": "1973",
      "unstructured": "Taha H (1973) Concave minimization over a convex polyhedron. Naval Res Logist Qu 20:533\u2013548",
      "journal-title": "Naval Res Logist Qu"
    },
    {
      "key": "BF01720068_CR40",
      "first-page": "106",
      "volume": "5",
      "author": "TV Thieu",
      "year": "1978",
      "unstructured": "Thieu TV (1978) Relationship between bilinear programming and concave minimization under linear constraints. Acta Math Vietnamica 5:106\u2013113",
      "journal-title": "Acta Math Vietnamica"
    },
    {
      "key": "BF01720068_CR41",
      "doi-asserted-by": "publisher",
      "first-page": "556",
      "DOI": "10.1287/moor.5.4.556",
      "volume": "5",
      "author": "NV Thoai",
      "year": "1980",
      "unstructured": "Thoai NV, Tuy H (1980) Convergent algorithms for minimizing a concave function. Math Oper Res 5:556\u2013566",
      "journal-title": "Math Oper Res"
    },
    {
      "key": "BF01720068_CR42",
      "first-page": "32",
      "volume": "159",
      "author": "H Tuy",
      "year": "1964",
      "unstructured": "Tuy H (1964) Concave programming under linear constraints. Dokl Adad Nauk SSSR 159:32\u201335 (Translated (1964): Soviet Math 5:1437-1440)",
      "journal-title": "Dokl Adad Nauk SSSR"
    },
    {
      "key": "BF01720068_CR43",
      "unstructured": "Tuy H (1982) Global maximization of a convex function over a closed, convex, not necessarily bounded set. Cahiers de Math\u00e9matiques de la D\u00e9cision No 8223, Universit\u00e9 Paris-Dauphine"
    },
    {
      "key": "BF01720068_CR44",
      "volume-title": "Global minimization of a difference of two convex functions",
      "author": "H Tuy",
      "year": "1983",
      "unstructured": "Tuy H (1983) Global minimization of a difference of two convex functions. Preprint, Institute of Mathematics, Hanoi"
    },
    {
      "key": "BF01720068_CR45",
      "unstructured": "Tuy H (1983) On outer approximation methods for solving concave minimization problems. Report Nr. 108, Forschungsschwerpunkt Dynamische Systeme, Universit\u00e4t Bremen"
    },
    {
      "key": "BF01720068_CR46",
      "doi-asserted-by": "publisher",
      "first-page": "147",
      "DOI": "10.1287/opre.15.1.147",
      "volume": "15",
      "author": "AF Veinott",
      "year": "1967",
      "unstructured": "Veinott AF (1967) The supporting hyperplane method for unimodal programming. Oper Res 15:147\u2013152",
      "journal-title": "Oper Res"
    },
    {
      "key": "BF01720068_CR47",
      "doi-asserted-by": "publisher",
      "first-page": "262",
      "DOI": "10.1287/opre.17.2.262",
      "volume": "17",
      "author": "AF Veinott",
      "year": "1969",
      "unstructured": "Veinott AF (1969) Minimum concave-cost solution of Leontief substitution models of multi-facility inventory systems. Oper Res 17:262\u2013291",
      "journal-title": "Oper Res"
    },
    {
      "key": "BF01720068_CR48",
      "doi-asserted-by": "publisher",
      "first-page": "486",
      "DOI": "10.1287/opre.14.3.486",
      "volume": "14",
      "author": "WI Zangwill",
      "year": "1966",
      "unstructured": "Zangwill WI (1966) A deterministic multi-product multifacility production and inventory model. Oper Res 14: 486\u2013507",
      "journal-title": "Oper Res"
    },
    {
      "key": "BF01720068_CR49",
      "unstructured": "Zhang XS, Rosen JB (1983) Global concave minimization. Discussion paper, Computer Science development, University of Minnesota"
    },
    {
      "key": "BF01720068_CR50",
      "doi-asserted-by": "publisher",
      "first-page": "1260",
      "DOI": "10.1287/opre.21.6.1260",
      "volume": "21",
      "author": "PB Zwart",
      "year": "1973",
      "unstructured": "Zwart PB (1973) Nonlinear programming: counterexamples to two global optimization algorithms. Oper Res 21:1260\u20131266",
      "journal-title": "Oper Res"
    },
    {
      "key": "BF01720068_CR51",
      "doi-asserted-by": "publisher",
      "first-page": "602",
      "DOI": "10.1287/opre.22.3.602",
      "volume": "22",
      "author": "PB Zwart",
      "year": "1974",
      "unstructured": "Zwart PB (1974) Global maximization of a convex function with linear inequality constraints. Oper Res 22:602\u2013609",
      "journal-title": "Oper Res"
    }
  ],
  "container-title": "Operations-Research-Spektrum",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF01720068.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/article/10.1007/BF01720068/fulltext.html",
      "content-type": "text/html",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF01720068.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    },
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF01720068",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2020,
        4,
        7
      ]
    ],
    "date-time": "2020-04-07T17:42:14Z",
    "timestamp": 1586281334000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "http://link.springer.com/10.1007/BF01720068"
    }
  },
  "subtitle": [
    "Introduction and survey"
  ],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1984,
        12
      ]
    ]
  },
  "references-count": 51,
  "journal-issue": {
    "issue": "4",
    "published-print": {
      "date-parts": [
        [
          1984,
          12
        ]
      ]
    }
  },
  "alternative-id": [
    "BF01720068"
  ],
  "URL": "http://dx.doi.org/10.1007/BF01720068",
  "relation": {},
  "ISSN": [
    "0171-6468",
    "1436-6304"
  ],
  "subject": [],
  "container-title-short": "OR Spektrum",
  "published": {
    "date-parts": [
      [
        1984,
        12
      ]
    ]
  }
}