Abstract
The development of efficient algorithms that provide all the local minima of a function is crucial to solve certain subproblems in many optimization methods. A “multi-local” optimization procedure using inexact line searches is presented, and numerical experiments are also reported. An application of the method to a semi-infinite programming procedure is included.
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Anderson, E.J. and Lewis, A.S. (1989) An extension of the simplex algorithm for semi-infinite linear programming.Mathematical Programming,44, 247–269.
Coope, I.D. and Watson, G.A. (1985) A projected lagrangian algorithm for semi-infinite programming.Mathematical Programming,32, 337–356.
Fletcher, R. (1987)Practical Methods of Optimization, 2n edition. John Wiley & sons. Chichester.
Goldstein, A.A. (1965) On steepest descent.SIAM J. Control,3, 147–151.
Hansen, P. (1992)Global Optimization using interval Analysis. Marcel Dekker, New York.
Hansen, P., Jaumard, B. and Lu, S.-H. (1992) Global optimization of univariate Lipschitz functions: I. Survey and properties.Mathematical Programmming,55, 251–272.
Horst, R. and Tuy, H. (1993)Global Optimization-Deterministic Approaches. Springer-Verlag, Berlin.
Leon, T. and Vercher, E. (1994) New descent rules for solving the linear semi-infinite programming problem.Operations Research Letters,15, 105–114.
Mayne, D.Q., Michalska, H. and Polak, E. (1994) An efficient algorithm for solving semi-infinite inequality problems with box constraints.Applied Mathematics Optimization,30, 135–157.
Panier, E.R. and Tits, A. (1989) A globally convergent algorithm with adaptively refined discretization for semi-infinite optimization problems arising in engineering design.IEEE Transactions on Automatic Control,34, 903–908.
Polak, E. (1987) On the Mathematical Foundations of Nondifferentiable Optimization in Engineering Design.SIAM Review,29, 21–89.
Polak, E. and He, L. (1991) Unified Steerable Phase I-Phase II Method of feasible Directions for Semi-infinite Optimization.Journal of Optimization Theory and Applications,69, 83–107.
Potra, F.A. and Shi, Y. (1995) Efficient Line Search Algorithm for Unconstrained Optimization.Journal of Optimization Theory and Applications,85, 677–704.
Price, C.J. and Coope, I.D. (1996) Numerical experiments in Semi-infinite Programming.Computational Optimization and Applications,6, 169–189.
Reemtsen, R. (1994) Some outer approximation methods for semi-infinite optimization problems.Journal of Computational and Applied Mathematics 53, 87–108.
Rinnooy Kan, A.G.H. and Timmer, G.T. (1989) Global Optimization. In: G.L. Nemhauser, A.G.H. Rinnooy Kan and M.J. Todd (eds)Optimization. North Holland, Amsterdam.
Roleff, R. (1979) A stable multiple exchange algorithm for linear SIP. In: R. Hettich (ed)Semi-infinite Programming. Springer, Berlin, 83–96.
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This work was partially supported by Ministerio de Educación y Ciencia, Spain, DGICYT grant PB93-0703. Author (*) was supported by the Consellería d'Educació i Ciència of the Generalitat Valenciana.
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León, T., Sanmatías, S. & Vercher, E. A multi-local optimization algorithm. Top 6, 1–18 (1998). https://doi.org/10.1007/BF02564795
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DOI: https://doi.org/10.1007/BF02564795