Related papers: Characterizations of the Aubin Property of the Sol…
This paper solves a fundamental open problem in variational analysis on the equivalence between the Aubin property and the strong regularity for nonlinear second-order cone programming (SOCP) at a locally optimal solution. We achieve this…
This paper characterizes the well-posedness of Karush-Kuhn-Tucker system for perturbed composite optimization. Using the parabolic regularity, we introduce a novel second-order variational function, shown to be the pivotal object governing…
This paper presents a perturbation analysis framework for nonsmooth optimization on connected Riemannian manifolds to bridge the gap between the rapid development of algorithmic approaches and a robust theoretical foundation. Using…
Sequential optimality conditions play an important role in constrained optimization since they provide necessary conditions without requiring constraint qualifications (CQs). This paper introduces a second-order extension of the Approximate…
Strong variational sufficiency is a newly proposed property, which turns out to be of great use in the convergence analysis of multiplier methods. However, what this property implies for non-polyhedral problems remains a puzzle. In this…
In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they…
In this work, we derive second-order optimality conditions for nonlinear semidefinite programming (NSDP) problems, by reformulating it as an ordinary nonlinear programming problem using squared slack variables. We first consider the…
This paper is devoted to studying the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a…
Second-order necessary optimality conditions for nonlinear conic programming problems that depend on a single Lagrange multiplier are usually built under nondegeneracy and strict complementarity. In this paper we establish a condition of…
In the last two decades, the sequential optimality conditions, which do not require constraint qualifications and allow improvement on the convergence assumptions of algorithms, had been considered in the literature. It includes the work by…
The paper deals with a new sharp criterion ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class includes parameter-dependent variational inequalities with non-polyhedral constraint sets…
Most numerical methods developed for solving nonlinear programming problems are designed to find points that satisfy certain optimality conditions. While the Karush-Kuhn-Tucker conditions are well-known, they become invalid when constraint…
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…
The asymptotic Karush-Kuhn-Tucker (AKKT) optimality conditions are distinguished from other approaches in the literature by virtue of their capacity to be effectively derived through numerical methods, such as the utilization of an…
In 2020, Yamakawa and Okuno proposed a stabilized sequential quadratic semidefinite programming (SQSDP) method for solving, in particular, degenerate nonlinear semidefinite optimization problems. The algorithm is shown to converge globally…
This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of…
This paper establishes the equivalence of the Aubin property and the strong regularity for generalized equations over $C^2$-cone reducible sets. This result resolves a long-standing question in variational analysis and extends the…
For general set-valued mappings, the Aubin property is ultimately tied to limiting coderivatives by the Mordukhovich criterion. Likewise, the existence of single-valued Lipschitzian localizations is related to strict graphical derivatives.…
We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general…
This paper concerns the tilt stability of local optimal solutions to a class of nonlinear semidefinite programs, which involves a twice continuously differentiable objective function and a convex feasible set. By leveraging the second…