Two methods for minimizing convex functions in a class of nonconvex sets. (Russian, English) Zbl 1199.90021

Zh. Vychisl. Mat. Mat. Fiz. 48, No. 10, 1802-1811 (2008); translation in Comput. Math. Math. Phys. 48, No. 10, 1768-1776 (2008).
Summary: The conditional gradient method and the steepest descent method, which are conventionally used for solving convex programming problems, are extended to the case where the feasible set is the set-theoretic difference between a convex set and the union of several convex sets. Iterative algorithms are proposed, and their convergence is examined.


90C26 Nonconvex programming, global optimization
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
30E15 Asymptotic representations in the complex plane
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