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2358. Calculating of weak subgradients and radial epiderivatives and applications in nonconvex and nonsmooth optimization

Invited abstract in session TC-41: Subgradient-based methods, stream Nonsmooth Optimization.

Tuesday, 12:30-14:00
Room: 97 (building: 306)

Authors (first author is the speaker)

1. Refail Kasimbeyli
Industrial Engineering, Eskisehir Technical University

Abstract

This work presents some calculus rules and new properties of the weak subgradients and the radial epiderivatives. The weak subgradient and the radial epiderivative concepts are based on the conical supporting methodology and therefore are able to characterize global behavior of a function under consideration and hence are used as a conical underestimation for nonconvex functions satisfying the Lipschitz condition from below. These generalized derivatives are used to establish global optimality conditions and to develop solution methods in nonconvex and nonsmooth optimization. Although the radial epiderivative concept can behave as the classical directional derivative in particular cases, it can be used to characterize and generate optimal solutions for many optimization problems that are impossible to handle with classical ones. In this work we present illustrative examples and demonstrate how the weak subgradients and the radial epiderivatives can be calculated for special classes of functions. The work presents applications for some classes of nonconvex and nonsmooth optimization problems.

Keywords

Status: accepted

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