Related papers: On local quasi efficient solutions for nonsmooth v…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
The paper is devoted to an analysis of optimality conditions for nonsmooth multidimensional problems of the calculus of variations with various types of constraints, such as additional constraints at the boundary and isoperimetric…
This work is concerned with an optimal control problem governed by a non-smooth quasilinear elliptic equation with a nonlinear coefficient in the principal part that is locally Lipschitz continuous and directionally but not G\^ateaux…
For evolutive Hamilton-Jacobi equations, we propose a refined definition of C^0-variational solution, adapted to Cauchy problems for continuous initial data. In this weaker framework we investigate the Markovian (or semigroup) property for…
The object of investigation in this paper are vector nonlinear programming problems with cone constraints. We introduce the notion of a Fritz John pseudoinvex cone-constrained vector problem. We prove that a problem with cone constraints is…
In this paper, we study federated optimization for solving stochastic variational inequalities (VIs), a problem that has attracted growing attention in recent years. Despite substantial progress, a significant gap remains between existing…
While Variational Inequality (VI) is a well-established mathematical framework that subsumes Nash equilibrium and saddle-point problems, less is known about its extension, Quasi-Variational Inequalities (QVI). QVI allows for cases where the…
This paper is focused on a stochastic quasi-variational inequality (SQVI) problem with a continuous and strongly-monotone mapping over a closed and convex set where the projection onto the constraint set may not be easy to compute. We…
We study the convergence issue for inexact descent algorithm (employing general step sizes) for multiobjective optimizations on general Riemannian manifolds (without curvature constraints). Under the assumption of the local…
This paper details a novel indirect method for solving constrained optimal control problems (OCPs) directly in continuous-time function space. The KKT conditions are embedded in a non-smooth complementarity function, which enables their…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
Approximate necessary optimality conditions in terms of Fr\'echet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective function are established with the aid of Ekeland's…
In the present paper, we focus on the vector optimization problems with inequality constraints, where objective functions and constrained functions are Fr\'echet differentiable, and whose gradient mapping is locally Lipschitz on an open…
We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function…
We present a derivative-based algorithm for nonlinearly constrained optimization problems that is tolerant of inaccuracies in the data. The algorithm solves a semi-smooth set of nonlinear equations that are equivalent to the first-order…
Non-convex optimization problems can be approximately solved via relaxation or local algorithms. For many practical problems such as optimal power flow (OPF) problems, both approaches tend to succeed in the sense that relaxation is usually…
As a starting point of our research, we show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to…
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and…
Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…
The main goal of this paper is developing the method of discrete approximations to derive necessary optimality conditions for a class of constrained sweeping processes with nonsmooth perturbations. Optimal control problems for sweeping…