A Parametric Optimization Point-Of-View of Comparison Functions
Assal\'e Adj\'e
TL;DR
This paper investigates the mathematical properties of parametric optimization problems related to comparison functions used in dynamical systems stability, focusing on positive definiteness, continuity, and level-boundedness.
Contribution
It provides new theoretical results on the positive definiteness, continuity, and level-boundedness of optimal value functions for generalized comparison functions.
Findings
Results on positive definiteness of the optimal value functions
Conditions for continuity of the optimal value functions
Analysis of level-boundedness in parametric optimization
Abstract
In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of special functions called comparison functions which arise in dynamical systems stability theory.
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Taxonomy
TopicsSimulation Techniques and Applications · Manufacturing Process and Optimization