In this paper, we give an overview on optimality conditions and exact penalization for the
mathematical program with switching constraints (MPSC). MPSC is a new class of …

Based on the tools of limiting variational analysis, we derive a sequential necessary
optimality condition for nonsmooth mathematical programs which holds without any …

As a starting point of our research, we show that, for a fixed order γ≥ 1, each local minimizer
of a rather general nonsmooth optimization problem in Euclidean spaces is either M …

Support vector machines (SVMs) are some of the most successful machine learning models
for binary classification problems. Their key idea is maximizing the margin from the data to …

For bilevel programmes with a convex lower-level programme, the classical approach
replaces the lower-level programme with its Karush-Kuhn-Tucker condition and solve the …

This paper is devoted to the study of the metric subregularity constraint qualification for
general optimization problems, with the emphasis on the nonconvex setting. We elaborate …

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 …

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 …

We develop new perturbation techniques for conducting convergence analysis of various
first-order algorithms for a class of nonsmooth optimization problems. We consider the …

Approximate necessary optimality conditions in terms of Frechet subgradients and normals
for a rather general optimization problem with a potentially non-Lipschitzian objective …