38. Weak subgradients and radial epiderivatives: calculus and optimization
Invited abstract in session FD-5: Structured nonsmooth optimization, stream Nonsmooth and nonconvex optimization algorithms.
Friday, 14:10 - 15:50Room: M:N
Authors (first author is the speaker)
| 1. | Refail Kasimbeyli
|
| Industrial Engineering, Eskisehir Technical University |
Abstract
Nonsmooth analysis has its origins in the early 1970s when nonlinear programmers attempted to deal with optimality conditions for problems with nonsmooth functions. The pointwise maximum or minimum of smooth functions are simple examples that can be considered as an illustration of nonsmoothness. In this paper, we study two kinds of generalized derivatives which allow us to investigate global optimal solutions of nonconvex and nondifferentiable optimization problems. These are the weak subgradient and the radial epiderivative concepts. Unlike the classical derivative and many generalized derivative concepts, the weak subgardient and the radial epiderivative concepts can be used to characterize global behaviour of objective functions in nonconvex and nonsmooth optimization. We present calculus rules for some classes of nondifferentiable functions and some applications in nonsmooth optimization. We establish a necessary and sufficient condition for global descent direction via the radial epiderivative. We believe that this condition can be used to develop a solution method for escaping from local minima. The paper also presents necessary and sufficient conditions for global optimum in nonconvex nonsmooth optimization by using the weak subgradients and the radial epiderivatives.
Keywords
- Convex and non-smooth optimization
- Derivative-free optimization
- Global optimization
Status: accepted
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