Related papers: Primal-Dual Stability in Local Optimality
We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the…
This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimizers for a broad class of…
Second-order optimality conditions of the bilevel programming problems are dependent on the second-order directional derivatives of the value functions or the solution mappings of the lower level problems under some regular conditions,…
A class of parametric optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is investigated. The perturbations appear in the objective functional, the state equation and in mixed pointwise…
This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We…
Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…
The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. H\"older or Lipschitz dependence of the optimal solution on perturbations are obtained for…
In this paper we present a new Lagrange dual problem associated to a primal DC optimization problem under the additivity condition (AC). As usual for DC programming, even weak duality is not guaranteed for free and, due to this issue, we…
This paper is concerned with first- and second-order optimality conditions as well as the stability for non-smooth semilinear optimal control problems involving the $L^1$-norm of the control in the cost functional. In addition to the…
Second-order sufficient conditions for local optimality have been playing an important role in local convergence analysis of optimization algorithms. In this paper, we demonstrate that this condition alone suffices to justify the linear…
Continuous time primal-dual gradient dynamics that find a saddle point of a Lagrangian of an optimization problem have been widely used in systems and control. While the global asymptotic stability of such dynamics has been well-studied, it…
We consider (stochastic) subgradient methods for strongly convex but potentially nonsmooth non-Lipschitz optimization. We provide new equivalent dual descriptions (in the style of dual averaging) for the classic subgradient method, the…
We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as…
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces.…
Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…
Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local…
We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand-side of the constraint system and the vector defining the objective function are subject to change. Using…
The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an…
We consider bilevel linear problems, where the right-hand side of the lower level problems is stochastic. The leader has to decide in a here-and-now fashion, while the follower has complete information. In this setting, the leader's outcome…
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex…