Vu Trung Hieu – Optimization Online

Weakly Homogeneous Optimization Problems

Published: 2020/01/28, Updated: 2020/02/17

Nonlinear Optimization asymptotic cone, boundedness, nonemptiness, optimization problem, pseudoconvex function, upper semincontinuity, weakly homogeneous function

This paper investigates a new class of optimization problems whose objective functions are weakly homogeneous relative to the constrain sets. Two sufficient conditions for nonemptiness and boundedness of solution sets are established. We also study linear parametric problems and upper semincontinuity of the solution map. Article Download View Weakly Homogeneous Optimization Problems

Dimension in Polynomial Variational Inequalities

Published: 2020/01/28

Vu Trung Hieu

Complementarity and Variational Inequalities dimension, polynomial fractional optimization, polynomial variational inequality, semialgebraic set, solution set

The aim of the paper is twofold. Firstly, by using the constant rank level set theorem from differential geometry, we establish sharp upper bounds for the dimensions of the solution sets of polynomial variational inequalities under mild conditions. Secondly, a classification of polynomial variational inequalities based on dimensions of their solution sets is introduced and … Read more