Concave Programming

Tuy, Hoang

[20] 1 805 488 Locatelli, Marco; Thoai, Nguyen V. Finite exact branch-and-bound algorithms for concave
minimization over polytopes. J. Global Optim. 18 (2000), no. 2, 107--128. 90C57 (90C26)

 pre990.48304 Holmberg, Kaj; Tuy, Hoang
A production-transportation problem with stochastic demand and concave production costs. (English)
Math. Program. 85A, No.1, 157-179 (1999). MSC 1991: *90C99

904.90156 Tuy, Hoang
Convex analysis and global optimization. (English)
Nonconvex Optimization and Its Applications. 22. Dordrecht: Kluwer Academic Publishers. xi, 339 p. Dfl. 240.00; \$ 136.00;
\sterling 80.00 (1998). MSC 1991: *90C30 49J52 49-02, Reviewer: J.F.Bonnans

 95i:90075 Horst, Reiner; Nguyen Van Thoai Constraint decomposition algorithms in global optimization. J. Global
Optim. 5 (1994), no. 4, 333--348. (Reviewer: Marlies Borchardt) 90C30 (65K05)

1 275 555 Tuy, H.; Ghannadan, S.; Migdalas, A.; Värbrand, P. Strongly polynomial algorithm for a
production-transportation problem with concave production cost. Optimization 27 (1993), no. 3, 205--227. 90C05 (90B06)

 88m:90139 Horst, R.; Tuy, H. On the convergence of global methods in multiextremal optimization. J. Optim.
Theory Appl. 54 (1987), no. 2, 253--271. (Reviewer: Petra Weidner) 90C31 (90C30)

87h:90175 Tuy, H.; Thieu, T. V.; Thai, Ng. Q. A conical algorithm for globally minimizing a concave function
over a closed convex set. Math. Oper. Res. 10 (1985), no. 3, 498--514. 90C25

H. Tuy,  Concave programming under linear constraints, Soviet Math 5 (1964), 1437-1440.

Hoffman, Karla L
88b:90100 Falk, James E.; Hoffman, Karla L. Concave minimization via collapsing polytopes. Oper. Res. 34 (1986),
no. 6, 919--929 (1987). 90C25

 82a:90116 Hoffman, Karla Leigh A method for globally minimizing concave functions over convex sets. Math.
Programming 20 (1981), no. 1, 22--32. (Reviewer: F. Weinberg) 90C25 (26B25 58C25)

   Rosen, J. B
  95a:90144 Phillips, A. T.; Rosen, J. B. Sufficient conditions for solving linearly constrained separable concave global
minimization problems. J. Global Optim. 3 (1993), no. 1, 79--94. (Reviewer: Vera V. Kova\u cevi\'c-Vuj\u ci\'c) 90C30

   92h:90082 Glick, J. H.; Maier, R. S.; Rosen, J. B. Parallel solution of large-scale, block-diagonal concave
maximization problems. SIAM J. Optim. 1 (1991), no. 4, 501--514. (Reviewer: K. Schittkowski) 90C06 (65K10 90C30)

  89j:90199 Phillips, A. T.; Rosen, J. B. A parallel algorithm for constrained concave quadratic global minimization.
Math. Programming 42 (1988), no. 2 (Ser. B), 421--448. 90C20 (65K05 65W05)

  88m:90107 Kalantari, B.; Rosen, J. B. An algorithm for global minimization of linearly constrained concave
quadratic functions. Math. Oper. Res. 12 (1987), no. 3, 544--561. 90C20 (65K05)

  88i:90140 Rosen, J. B.; Pardalos, P. M. Global minimization of large-scale constrained concave quadratic problems
by separable programming. Math. Programming 34 (1986), no. 2, 163--174. (Reviewer: Ulrich Eckhardt) 90C20 (65K05)

Bomze, Immanuel M
 95a:90054 Bomze, Immanuel M.; Danninger, Gabriele A global optimization algorithm for concave quadratic
programming problems. SIAM J. Optim. 3 (1993), no. 4, 826--842. (Reviewer: Yahya Fathi) 90C20 (65K05)

  94j:90061 Danninger, Gabriele; Bomze, Immanuel M. Using copositivity for global optimality criteria in concave
quadratic programming problems. Math. Programming 62 (1993), no. 3, Ser. A, 575--580. 90D26 (49J52)

Engel, Olaf
95g:90070 90C30
Borchardt, Marlies(D-ILTU); Engel, Olaf(D-ILTU)
A counterexample to a global optimization algorithm. (English. English summary)
J. Global Optim. 5 (1994), no. 4, 371--372.

    98m:90173 Horst, R.; Thoai, N. V. An integer concave minimization approach for the minimum concave cost
capacitated flow problem on networks. OR Spektrum 20 (1998), no. 1, 47--53. 90C35

 96m:90056 Horst, R.; Nast, M. Linearly constrained global minimization of functions with concave minorants. J.
Optim. Theory Appl. 88 (1996), no. 3, 751--763. (Reviewer: Laura Martein) 90C26 (90C30)

 95e:90075 Horst, R.; Muu, L. D.; Nast, M. Branch-and-bound decomposition approach for solving
quasiconvex-concave programs. J. Optim. Theory Appl. 82 (1994), no. 2, 267--293. (Reviewer: Zeng Kun Xu) 90C26

    93h:90085 Horst, R.; Thoai, N. V. Conical algorithm for the global minimization of linearly constrained
decomposable concave minimization problems. J. Optim. Theory Appl. 74 (1992), no. 3, 469--486. (Reviewer: Panos M.
Pardalos) 90C30 (65K10)

   93c:90072 Al-Khayyal, Faiz A.; Horst, Reiner; Pardalos, Panos M. Global optimization of concave functions
subject to quadratic constraints: an application in nonlinear bilevel programming. Hierarchical optimization. Ann. Oper. Res.
34 (1992), no. 1-4, 125--147. (Reviewer: Jan Rückmann) 90C30 (90C20 90C31)

    92f:90056 Benson, Harold P.; Horst, Reiner A branch and bound--outer approximation algorithm for concave
minimization over a convex set. Comput. Math. Appl. 21 (1991), no. 6-7, 67--76. (Reviewer: R. N. Kaul) 90C30 (65K10)

   92c:90103 Horst, Reiner; Thoai, Nguyen V.; Benson, Harold P. Concave minimization via conical partitions and
polyhedral outer approximation. Math. Programming 50 (1991), no. 2 (Ser. A), 259--274. (Reviewer: Pierre Loridan) 90C30
(65K10 90C26)

     90j:90119 Horst, R.; Thoai, N. V. Modification, implementation and comparison of three algorithms for globally
solving linearly constrained concave minimization problems. Computing 42 (1989), no. 2-3, 271--289. (Reviewer: Fanos
Pinter) 90C30

    89m:90140 Tuy, Hoang; Horst, Reiner Convergence and restart in branch-and-bound algorithms for global
optimization. Application to concave minimization and D.C. optimization problems. Math. Programming 41 (1988), no. 2
(Ser. A), 161--183. (Reviewer: J. Mockus) 90C30 (90C25)

     89i:90073 Horst, R. Deterministic global optimization with partition sets whose feasibility is not known: application
to concave minimization, reverse convex constraints, DC-programming, and Lipschitzian optimization. J. Optim. Theory
Appl. 58 (1988), no. 1, 11--37. (Reviewer: Hoàng T\udot uy) 90C30 (65K05)

595.90079 Horst, R.; Tuy, H.
On the convergence of global methods in multiextremal optimization. (English)
J. Optimization Theory Appl. 54, 253-271 (1987). MSC 1991: *90C31 90C30

 581.90073    88b:90110 Horst, R. A general class of branch-and-bound methods in global optimization with some new
approaches for concave minimization. J. Optim. Theory Appl. 51 (1986), no. 2, 271--291. (Reviewer: R. \c Serban) 90C30

     86d:90111 Horst, R. On the global minimization of concave functions. Introduction and survey. OR Spektrum 6
(1984), no. 4, 195--205. 90C25

    1 465 314 Horst, R.; Thoai, N. V. Erratum: "Modification, implementation and comparison of three algorithms for
globally solving linearly constrained concave minimization problems" [Computing {42} (1989), no. 2-3, 271--289; MR
90j:90119]. Computing 59 (1997), no. 1, 94. 90C30

    1 390 524 Horst, Reiner; Nguyen Van Thoai Global minimization of separable concave functions under linear
constraints with totally unimodular matrices. State of the art in global optimization (Princeton, NJ, 1995), 35--45,
Nonconvex Optim. Appl., 7, Kluwer Acad. Publ., Dordrecht, 1996. 90C26

    837 442 Horst, Reiner Konkave Minimierungsprobleme in Operations Research. (German) [Concave minimization
problems in operations research] Operations research proceedings 1981 (Göttingen), 580--591, Springer, Berlin, 1982.

On algorithms for solving concave minimization problems, Sep 29, 1988  Penn State Comp Sci Coll.

 (Z614.90094), Z604.90114).

Vaserstein, L. N
53 #15379 90C30  Vaserstein, L. N.; Chmil' , V. I.;  Sherman, E. B.
A multi-extremal problem for the growth and location of production with a concave objective function. (Russian)
Mathematical methods in economic research (Russian), pp. 138--143.
Izdat. "Nauka", Moscow, 1974.

   92f:90056 Benson, Harold P.; Horst, Reiner A branch and bound--outer approximation algorithm for concave
minimization over a convex set. Comput. Math. Appl. 21 (1991), no. 6-7, 67--76. (Reviewer: R. N. Kaul) 90C30 (65K10)

  89k:90148 Utkin, S. L.; Khachaturov, V. R.; Khoang, Tu\u\i Conical algorithms for solving the concave
programming problem and some of its generalizations. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 28 (1988), no. 7, 992--999,
1117. (Reviewer: S. Zlobec) 90C30

  87k:90240 Vasil\cprime ev, N. S. Necessary and sufficient conditions for the global minimum in concave
problems. (Russian) Optimization and control, 84--89, Moskov. Gos. Univ., Moscow, 1985. (Reviewer: I. Maru\c sciac)
90C30 (90C25)

 87h:90172 Bu\u\i Tkhe Tam; Vu Tkhien Ban Minimization of a concave function with linear constraints.
(Russian) Èkonom. i Mat. Metody 21 (1985), no. 4, 709--714. (Reviewer: I. Maru\c sciac) 90C25

  87d:90128 Einbu, John M. Addendum: a finite algorithm for solving nonlinear allocation problems: "A finite
method for the solution of a multiresource allocation problem with concave return functions" [Math. Oper. Res. {9} (1984),
no. 2, 232--243; MR 85h:90082]. Math. Oper. Res. 10 (1985), no. 1, 154--157. (Reviewer: Roman S\l owi\'nski) 90C25

    87b:90046 Leopoulos, V. I.; Proth, J.-M. Le problème multi-produits avec coûts concaves et incitation aux
lancements groupés: le cas général. (French) [The multiproduct model with concave costs and joint production costs: the
general case] RAIRO Automat.-Prod. Inform. Ind. 19 (1985), no. 2, 117--130. (Reviewer: L. C. Thomas) 90B05

 Zh.Vych.Mat.& Mat.fiz. 25:2 (1985).. 

Porembski, Marcus
     CMP 1 641 415 (99:01) 90C30   Porembski, Marcus(D-MRBG)
Decomposition cuts---a new way to derive deep cutting planes in global optimization.
Operations Research Proceedings 1997 (Jena), 68--73,
Springer, Berlin, 1998.

How to extend the concept of convexity cuts to derive deeper cutting planes, J Global Opt 15 (1999), 371-404.

Strategies for a finite and exact cutting plane algorithm for concave minimization, preprint.

Finitely convergent cutting planes for concave minimization, preprint.