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Deterministic methods in constrained global optimization: Some recent advances and new fields of application

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  • Reiner Horst

Abstract

Recent developments in deterministic global optimization methods have considerably enlarged the fields of optimization where those methods can be successfully applied. It is the purpose of the present article to give a brief survey of both some of the most promising methods and new fields of application. The methods considered comprise branch and bound and outer approximation as well as combinations of branch and bound with outer approximation. The fields of applications to be discussed include concave minimization, reverse convex programming, d.c. programming, Lipschitzian optimization, systems of equations, and (or) inequalities and global integer programming.

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  • Reiner Horst, 1990. "Deterministic methods in constrained global optimization: Some recent advances and new fields of application," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 433-471, August.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:4:p:433-471
    DOI: 10.1002/1520-6750(199008)37:43.0.CO;2-2
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    1. James E. Falk & Karla R. Hoffman, 1976. "A Successive Underestimation Method for Concave Minimization Problems," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 251-259, August.
    2. A. Victor Cabot, 1974. "Variations on a cutting plane method for solving concave minimization problems with linear constraints," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 21(2), pages 265-274, June.
    3. Claude‐Alain Burdet, 1973. "Polaroids: A new tool in non‐convex and in integer programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(1), pages 13-24, March.
    4. Masao Fukushima, 1983. "An Outer Approximation Algorithm for Solving General Convex Programs," Operations Research, INFORMS, vol. 31(1), pages 101-113, February.
    5. Mary W. Cooper, 1981. "A Survey of Methods for Pure Nonlinear Integer Programming," Management Science, INFORMS, vol. 27(3), pages 353-361, March.
    6. S. Selcuk Erenguc & Harold P. Benson, 1986. "The interactive fixed charge linear programming problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(2), pages 157-177, May.
    7. R. J. Hillestad, 1975. "Optimization Problems Subject to a Budget Constraint with Economies of Scale," Operations Research, INFORMS, vol. 23(6), pages 1091-1098, December.
    8. B. Kalantari & J. B. Rosen, 1987. "An Algorithm for Global Minimization of Linearly Constrained Concave Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 544-561, August.
    9. James E. Falk & Karla L. Hoffman, 1986. "Concave Minimization Via Collapsing Polytopes," Operations Research, INFORMS, vol. 34(6), pages 919-929, December.
    10. Fred Glover, 1973. "Convexity Cuts and Cut Search," Operations Research, INFORMS, vol. 21(1), pages 123-134, February.
    11. Harold P. Benson, 1985. "A finite algorithm for concave minimization over a polyhedron," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 32(1), pages 165-177, February.
    12. James E. Falk & Richard M. Soland, 1969. "An Algorithm for Separable Nonconvex Programming Problems," Management Science, INFORMS, vol. 15(9), pages 550-569, May.
    13. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    14. W.W. Hogan, 1973. "Boxstep: A New Strategy for Large Scale Mathematical Programming," Discussion Papers 46, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    15. James E. Falk, 1973. "Technical Note—Conditions for Global Optimality in Nonlinear Programming," Operations Research, INFORMS, vol. 21(1), pages 337-340, February.
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    3. E. Demidenko, 2008. "Criteria for Unconstrained Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 375-395, March.
    4. Harold P. Benson, 1996. "Deterministic algorithms for constrained concave minimization: A unified critical survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 765-795, September.
    5. Vanhoucke, Mario & Demeulemeester, Erik & Herroelen, Willy, 2003. "Progress payments in project scheduling problems," European Journal of Operational Research, Elsevier, vol. 148(3), pages 604-620, August.

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