solution set – Optimization Online

Dimension in Polynomial Variational Inequalities

Published: 2020/01/28

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

Some criteria for error bounds in set optimization

Published: 2012/08/03, Updated: 2012/08/29

Xuan Duc Ha Truong

Multi-Criteria Optimization, Nonsmooth Optimization coderivative, constraint set, error bound, henig efficient solution, metric subregularity, pareto efficient solution, set-valued optimization problem, solution set, subdifferential, super efficient solution

We obtain sufficient and/or necessary conditions for global/local error bounds for the distances to some sets appeared in set optimization studied with both the set approach and vector approach (sublevel sets, constraint sets, sets of {\it all } Pareto efficient/ Henig proper efficient/super efficient solutions, sets of solutions {\it corresponding to one} Pareto efficient/Henig proper … Read more