{epsilon}-optimality conditions for weakly convex problems
There are several generalizations concerning the concept of convexity both for sets and for functions. Weak convexity, among these, has showed many possibilities of applications and many theoretical properties. It has, in fact, been applied in several fields of mathematics: see for example geometry and optimization. We want to analyze this generalization of the concept of convexity via the image-space approach. This kind of approach has showed its utility in many fields of optimization. In particular, we introduce a new concept of {open_quotes}image{close_quotes} based on a suitable relaxation or reduction (lower and upper) of the image itself. Moreover we analyze the main properties of this concept and we show how to utilize it in the study of weakly convex constrained extremum problems in order to obtain {epsilon}-optimality conditions. The paper is divided in three parts: in the first we introduce the concept of perturbed image and we investigate the main theoretical properties. In the second we state {epsilon}-optimality conditions for weakly convex constrained extremum problems. In the third one we study relationships between this type of image and the augmented lagrangian.
- OSTI ID:
- 36363
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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