Relations between invex concepts
It is well known that many properties of convex optimization problems, especially sufficient conditions for optimality, and duality properties, are preserved when {open_quotes}convex{close_quotes} is weakened to {open_quotes}invex{close_quotes}. However, there are several distinct {open_quotes}invex{close_quotes} properties - invex at a point, in a region, or convexifiable by a transformation, and these are not equivalent. It is now shown that a generalization of {open_quotes}pre-invex{close_quotes} characterizes invex at a point, and a further generalization characterizes the convexifiable property. These versions do not require any derivatives. Another generalization, {open_quotes}strengthened invex{close_quotes}, implies that a Karush-Kuhn-Tucker point is a strict minimum, a property that is preserved under small perturbations of the problem.
- OSTI ID:
- 35926
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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