Second-Order Optimality Conditions for Nonconvex Set-Constrained Optimization…

In this paper, we study second-order optimality conditions for nonconvex set-constrained optimization problems. For a convex set-constrained optimization problem, it is well known that second-order…

Directional Necessary Optimality Conditions for Bilevel Programs

The bilevel program is an optimization problem in which the constraint involves solutions to a parametric optimization problem. It is well known that the value function reformulation provides an eq…

Generic Property of the Partial Calmness Condition for Bilevel Programming Pr…

The partial calmness for the bilevel programming problem (BLPP) is an important condition which ensures that a local optimal solution of BLPP is a local optimal solution of a partially penalized pr…

A Lagrange Multiplier Expression Method for Bilevel Polynomial Optimization

This paper studies bilevel polynomial optimization. We propose a method to solve it globally by using polynomial optimization relaxations. Each relaxation is obtained from the Karush--Kuhn--Tucker …

Exact Formula for the Second-Order Tangent Set of the Second-Order Cone Compl…

Directional Quasi-/Pseudo-normality as Sufficient Conditions for Metric Subre…

Bilevel Polynomial Programs and Semidefinite Relaxation Methods

Minimizing the condition number of a gram matrix

Necessary Optimality Conditions for Multiobjective Bilevel Programs

New necessary optimality conditions for bilevel programs by combining the MPE…