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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…

Optimization and Control · Mathematics 2026-04-24 Jiguang Yu

In this paper, we consider the {\it generalized polynomial complementarity problem} (GPCP), which covers the recently introduced {\it polynomial complementarity problem} (PCP) and the well studied {\it tensor complementarity problem} (TCP)…

Optimization and Control · Mathematics 2019-05-03 Liyun Ling , Chen Ling , Hongjin He

In this paper, we study the stochastic linear complementarity problems on extended second order cones (stochastic ESOCLCP). We first convert the problem to a stochastic mixed complementarity problem on the nonegative orthant (SMixCP).…

Optimization and Control · Mathematics 2019-11-04 Sándor Zoltán Németh , Lianghai Xiao

We provide a framework for obtaining error bounds for linear conic problems without assuming constraint qualifications or regularity conditions. The key aspects of our approach are the notions of amenable cones and facial residual…

Optimization and Control · Mathematics 2021-09-27 Bruno F. Lourenço

The proximal, regular and limiting normal cones to the second-order cone complementarity set play important roles in studying mathematical programs with second-order cone complementarity constraints, second-order cone programs, and the…

Optimization and Control · Mathematics 2016-05-25 Jane J. Ye , Jinchuan Zhou

We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This framework goes beyond the classical Lipschitzian and H\"olderian error bounds and includes…

Optimization and Control · Mathematics 2023-10-20 Tianxiang Liu , Bruno F. Lourenço

A new error bound for the linear complementarity problem is given when the involved matrix is a B-matrix. It is shown that this bound is sharper than some previous bounds [C.Q. Li, Y.T. Li. Note on error bounds for linear complementarity…

Numerical Analysis · Mathematics 2016-03-01 Chaoqian Li , Mengting Gan , Shaorong Yang

This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T…

Optimization and Control · Mathematics 2011-02-07 M. J. CÁnovas , M. A. LÓpez , B. S. Mordukhovich , J. Parra

A new error bound for the linear complementarity problem when the matrix involved is a B-matrix is presented, which improves the corresponding result in [C.Q. Li et al., A new error bound for linear complementarity problems for B-matrices.…

Numerical Analysis · Mathematics 2016-10-21 Lei Gao , Chaoqian Li

Rank-constrained matrix problems appear frequently across science and engineering. The convergence analysis of iterative algorithms developed for these problems often hinges on local error bounds, which correlate the distance to the…

Optimization and Control · Mathematics 2025-10-03 Ruoning Chen , Defeng Sun , Liping Zhang

Neural network (NN) approximations of model predictive control (MPC) are a versatile approach if the online solution of the underlying optimal control problem (OCP) is too demanding and if an exact computation of the explicit MPC law is…

Systems and Control · Electrical Eng. & Systems 2024-07-10 Dieter Teichrib , Moritz Schulze Darup

Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…

Optimization and Control · Mathematics 2018-12-06 A Uderzo

This paper presents a posteriori error estimates for conforming numerical approximations of eigenvalue clusters of second-order self-adjoint elliptic linear operators with compact resolvent. Given a cluster of eigenvalues, we estimate the…

Numerical Analysis · Mathematics 2020-08-11 Eric Cancès , Geneviève Dusson , Yvon Maday , Benjamin Stamm , Martin Vohralík

In this paper, stability and sensitivity properties of a class of parametric constrained optimization problem, whose feasible region is defined by a set-valued inclusion, are investigated through the associated optimal value function.…

Optimization and Control · Mathematics 2024-12-06 Amos Uderzo

This paper establishes error bounds for the convergence of a piecewise linear approximation of the constrained optimal smoothing problem posed in a reproducing kernel Hilbert space (RKHS). This problem can be reformulated as a Bayesian…

Statistics Theory · Mathematics 2025-06-24 Laurence Grammont , François Bachoc , Andrés F. López-Lopera

We derive global estimates for the error in solutions of linear hyperbolic systems due to inaccurate boundary geometry. We show that the error is bounded by data and bounded in time when the solutions in the true and approximate domains are…

Numerical Analysis · Mathematics 2025-03-27 David A. Kopriva , Andrew R. Winters , Jan Nordström

We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…

Information Theory · Computer Science 2018-08-28 Chao Tian

The presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of stability analysis or bilevel optimization. An example of such a Lipschitzian property…

Optimization and Control · Mathematics 2020-12-17 Patrick Mehlitz , Leonid I. Minchenko

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…

Optimization and Control · Mathematics 2024-07-29 Jiawei Chen , Luyu Liu , Yibing Lv , Kequan Zhao

Relaxed constant positive linear dependence constraint qualification (RCPLD) for a system of smooth equalities and inequalities is a constraint qualification that is weaker than the usual constraint qualifications such as Mangasarian…

Optimization and Control · Mathematics 2020-03-24 Mengwei Xu , Jane J. Ye