相关论文: Differential stability of convex optimization prob…

This paper considers the equilibrium-free stability and performance analysis of discrete-time nonlinear systems. We consider two types of equilibrium-free notions. Namely, the universal shifted concept, which considers stability and…

In this note we explore duality in reverse convex optimization with reverse convex inequality constraints. While we are examining the special case of a finite index set of the inequality constraints, we are primarily interested in the…

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.…

We investigate the stability of the equilibrium-induced optimal value in one-dimensional diffusion setting for a time-inconsistent stopping problem under non-exponential discounting. We show that the optimal value is semi-continuous with…

Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…

The Convex Envelope of a given function was recently characterized as the solution of a fully nonlinear Partial Differential Equation (PDE). In this article we study a modified problem: the Dirichlet problem for the underlying PDE. The main…

New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable…

In the first part, we discuss the stability of the strong slope and of the subdifferential of a lower semicontinuous function with respect to Wijsman perturbations of the function, i.e. perturbations described via Wijsman convergence. In…

A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…

We derive stability criteria for saddle points of a class of nonsmooth optimization problems in Hilbert spaces arising in PDE-constrained optimization, using metric regularity of infinite-dimensional set-valued mappings. A main ingredient…

We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…

We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized…

In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…

Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…

This paper is concerned with the directional derivative of the value function for a very general set-constrained optimization problem under perturbation. Under reasonable assumptions, we obtain upper and lower estimates for the upper and…

We study the integrality gap of convex mixed-integer programs, that is, the difference between the optimal value of such a problem and the optimal value of its continuous relaxation. We study classes of convex sets whose associated…

This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…

This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints…

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…

Modeling parts of an optimization problem as an optimal value function that depends on a top-level decision variable is a regular occurrence in optimization and an essential ingredient for methods such as Benders Decomposition. It often…