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

Chernyaev, Yu. A.

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.

MSC:

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

Keywords:

\(\epsilon\)-stationary point; conventional \(\epsilon\)-subdifferential; necessary condition of local minimum