Related papers: A Globally Convergent Method for Computing B-stati…
We present a new framework for the solution of mathematical programs with equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is viewed as a concentration of an unconstrained optimization which minimizes the…
This study explores B-stationarity of mathematical programs with complementarity constraints (MPCCs) and convergence behavior of MPCC algorithms. Special attention is given to the cases with biactive complementarity constraints. First, we…
Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
In this workshop, we discuss several algorithms for mathematical programs with equilibrium constraints (MPECs). The unifying theme is that MPECs are optimization problems whose feasible set contains a lower-level equilibrium system, often…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…
Constraint qualifications for a Mathematical Program with Equilibrium Constraints (MPEC) are essential for analyzing stationarity properties and establishing convergence results. In this paper, we explore several classical MPEC constraint…
In this paper, we study the mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with a parametric generalized equation involving the regular normal cone. We derive a new necessary optimality…
We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical nonlinear programming techniques. The goal is twofold. First,…
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…
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…
In this paper we begin by discussing the simple bilevel programming problem (SBP) and its extension the simple mathematical programming problem under equilibrium constraints (SMPEC). Here we first define both these problems and study their…
Coordinate descent algorithms are widely used in machine learning and large-scale data analysis due to their strong optimality guarantees and impressive empirical performance in solving non-convex problems. In this work, we introduce Block…
Our recent study (Lin and Ohtsuka, 2024) proposed a new penalty method for solving mathematical programming with complementarity constraints (MPCC). This method first reformulates MPCC as a parameterized nonlinear programming called gap…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
This paper proposes a joint decomposition method that combines La- grangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global…
This paper proposes a constrained maximum likelihood estimator for sequential search models, using the MPEC (Mathematical Programming with Equilibrium Constraints) approach. This method enhances numerical accuracy while avoiding ad hoc…
Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A…
In this paper, we propose a a gradient-based neural network model to solve the mathematical programming problems with complementary constraints (MPCC). In order to facilitate tractable optimization, the problem MPCC is transformed via a…