Abstract
A new approach to the solution of nonconvex problems of optimal control and mathematical programming is treated, which rests on the theory of global optimality conditions (GOC). Moreover, attention is given to the development and investigation of special methods of local search and to investigation of the convergence of strategies of global search, which rely on the GOCs, and also to a comparable numerical experiment.
Similar content being viewed by others
REFERENCES
Vasil'ev, F.P., Metody optimizatsii (Optimization Methods), Moscow: Factorial Press, 2002.
Polyak, B.T., Vvedenie v optimizatsiyu (Introduction to Optimization), Moscow: Nauka, 1983.
Horst, R. and Tuy, H., Global Optimization (Deterministic Approaches), Berlin: Springer-Verlag, 1993.
Hiriart-Urruty, J.B., From Convex Optimization to Nonconvex Optimization. Part 1: Necessary and Sufficient Conditions for Global Optimality, in Nonsmooth Optimization and Related Topic, Clarke,F.H., et al., Eds., New York: Plenum, 1989.
Strekalovsky, A.S. and Vasiliev, I.L., On Global Search for Nonconvex Optimal Control Problems. Developments in Global Optimization, in Nonconvex Optimization and its Applications, Bomze, I.M., et al., Eds., Dordrecht: Kluwer Academic, 1997.
Srochko, V.A., Iteratsionnye metody resheniya zadach optimal'nogo upravleniya (Iterative Methods for the Solution of Optimal Control Problems), Moscow: Fizmatlit, 2000.
Strekalovsky, A.S., On Extremal Problems in Complements of Convex Sets, Kibern. Sist. Analiz., 1993, no. 1, pp. 113–126.
Strekalovsky, A.S., On Extremal Problems with d.c. Constraints, Zh. Vychisl. Mat. Mat. Fiz., 2001, vol. 41, no. 12, pp. 1833–1843.
Strekalovsky, A.S., On Global Maximum of a Convex Terminal Functional in Optimal Control Problems, J. Global Optimiz., 1995, no. 7, pp. 75–91.
Strekalovsky, A.S. and Tsevendorj, I., Testing the ℜ-Strategy for a Reverse-Convex Problem, J. Global Optimiz., 1998, vol. 13, no. 1, pp. 61–74.
Strekalovsky, A.S. and Kuznetsova, A.A., On Solving the Maximum Clique Problem, J. Global Optimiz., 2001, vol. 21, no. 3, pp. 265–288.
Strekalovsky, A.S., Kuznetsova, A.A., and Yakovleva, T.V., On the Numerical Solution of Nonconvex Optimization Problems, Sib. Zh. Vychisl. Mat., 2001, vol. 4, no. 2, pp. 185–199.
Strekalovsky, A.S., On Minimization of the Difference of Two Convex Functions on an Admissible Set, Zh. Vychisl. Mat. Mat. Fiz., 2003, vol. 43, no. 3, pp. 399–409.
Strekalovsky, A.S., Elementy nevypukloi optimizatsii (Elements of Nonconvex Optimization), Novosibirsk: Nauka, 2003.
Rosen, J.B., Iterative Solution of Nonlinear Optimal Control Problems, SIAM J. Control, 1966, vol. 4, pp. 223–244.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Strekalovsky, A.S., Yakovleva, T.V. On a Local and Global Search Involved in Nonconvex Optimization Problems. Automation and Remote Control 65, 375–387 (2004). https://doi.org/10.1023/B:AURC.0000019368.45522.7a
Issue Date:
DOI: https://doi.org/10.1023/B:AURC.0000019368.45522.7a