相关论文: Relations between Abs-Normal NLPs and MPCCs. Part …

We consider the Mathematical Program with Complementarity Constraints (MPCC). One of the main challenges in solving this problem is the systematic failure of standard Constraint Qualifications (CQs). Carefully accounting for the…

The cardinality constrained optimization problem (CCOP) is an optimization problem where the maximum number of nonzero components of any feasible point is bounded. In this paper, we consider CCOP as a mathematical program with disjunctive…

The constant rank constraint qualification (CRCQ) for second-order cone programs, introduced by Andreani et al. in [Math. Program. 202 (2023), 473 - 513], shares some desirable properties with its classical nonlinear programming…

In this paper, we investigate second-order necessary conditions and exact penalty of mathematical programs with switching constraints (MPSC). Some new second-order constraint qualifications and second-order quasi-normality are introduced…

For an arbitrary finite family of semi-algebraic/definable functions, we consider the corresponding inequality constraint set and we study qualification conditions for perturbations of this set. In particular we prove that all positive…

The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of…

In this paper, we consider the constraint set $K$ of inequalities with nonsmooth nonconvex constraint functions. We show that under Abadie's constraint qualification the "perturbation property" of the best approximation to any $x$ in $\R^n$…

Our study is motivated by the solution of Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique, an iterative method whose main characteristic is that of solving,…

Mathematical programs with vanishing constraints (MPVCs) are a class of nonlinear optimization problems with applications to various engineering problems such as truss topology design and robot motion planning. MPVCs are difficult problems…

Mathematical programs with complementarity constraints (MPCCs) are a challenging class of nonlinear optimization problems, because their nonlinear programming reformulations violate standard constraint qualifications at every feasible…

A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…

We introduce a constraint qualification condition (GPMFCQ) for smooth infinite programming problems, where the nonlinear operator defining the equality constraints has nonsurjective derivative at the local minimum. The condition is a…

In this paper, we study the regularity assumptions commonly adopted in bilevel optimization with constrained lower-level problems, including the linear independence constraint qualification, the strict complementary slackness condition, and…

This article is divided into two parts. In the first part, we examine the Brezis-Oswald problem involving a mixed anisotropic and nonlocal $p$-Laplace operator. We establish results on existence, uniqueness, boundedness, and the strong…

Asymptotic stationarity and regularity conditions turned out to be quite useful to study the qualitative properties of numerical solution methods for standard nonlinear and complementarity-constrained programs. In this paper, we first…

Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint…

In this workshop, we present a compact but rigorous introduction to second-order optimality conditions for mathematical programs with equilibrium constraints (MPECs). We start from the classical nonlinear programming template, then explain…

When dealing with general Lipschitzian optimization problems, there are many problem classes where even weak constraint qualifications fail at local minimizers. In contrast to a constraint qualification, a problem qualification does not…

This paper examines solution methods for mathematical programs with complementarity constraints (MPCC) obtained from the time-discretization of optimal control problems (OCPs) subject to nonsmooth dynamical systems. The MPCC theory and…

Recently, we proposed a class of inequalities called lifted bilinear cover inequalities, which are second-order cone representable convex inequalities, and are valid for a set described by a separable bilinear constraint together with…