相关论文: Shape Derivative for Penalty-Constrained Nonsmooth…

This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…

Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of the constraints. We first propose an equivalent optimization…

The present article is dedicated to proving convergence of the stochastic gradient method in case of random shape optimization problems. To that end, we consider Bernoulli's exterior free boundary problem with a random interior boundary. We…

We develop two new proximal alternating penalty algorithms to solve a wide range class of constrained convex optimization problems. Our approach mainly relies on a novel combination of the classical quadratic penalty, alternating…

The present work investigates the segmentation of textures by formulating it as a strongly convex optimization problem, aiming to favor piecewise constancy of fractal features (local variance and local regularity) widely used to model…

A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…

We consider a general decomposable convex optimization problem. By using right-hand side allocation technique, it can be transformed into a collection of small dimensional optimization problems. The master problem is a convex non-smooth…

This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…

Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…

We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…

In this article, we consider the problem of optimal design of a compliant structure under a volume constraint, within the framework of linear elasticity. We introduce the pure displacement and the dual mixed formulations of the linear…

Shape calculus concerns the calculation of directional derivatives of some quantity of interest, typically expressed as an integral. This article introduces a type of shape calculus based on localized dilation of boundary faces through…

This article combines various methods of analysis to draw a comprehensive picture of penalty approximations to the value, hedge ratio, and optimal exercise strategy of American options. While convergence of the penalised solution for…

We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously…

The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

In this paper we discuss a level set approach for the identification of an unknown boundary in a computational domain. The problem takes the form of a Bernoulli problem where only the Dirichlet datum is known on the boundary that is to be…

In this paper, we study a variant of the quadratic penalty method for linearly constrained convex problems, which has already been widely used but actually lacks theoretical justification. Namely, the penalty parameter steadily increases…

For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…

We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…