Related papers: Nonsmooth convex-concave saddle point problems wit…
This is a continuation of our previous work entitled \enquote{Alternating Proximity Mapping Method for Convex-Concave Saddle-Point Problems}, in which we proposed the alternating proximal mapping method and showed convergence results on the…
Many problems in high-dimensional statistics and optimization involve minimization over nonconvex constraints-for instance, a rank constraint for a matrix estimation problem-but little is known about the theoretical properties of such…
This paper introduces a class of two-stage stochastic minimax problems where the first-stage objective function is nonconvex-concave while the second-stage objective function is strongly convex-concave. We establish properties of the…
We analyze the behavior of randomized coordinate gradient descent for nonconvex optimization, proving that under standard assumptions, the iterates almost surely escape strict saddle points. By formulating the method as a nonlinear random…
This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…
In this paper, we consider a class of sparse regression problems, whose objective function is the summation of a convex loss function and a cardinality penalty. By constructing a smoothing function for the cardinality function, we propose a…
We study the minimax problem $\min_{x\in M} \max_y f_r(x,y):=f(x,y)-h(y)$, where $M$ is a compact submanifold, $f$ is continuously differentiable in $(x, y)$, $h$ is a closed, weakly-convex (possibly non-smooth) function and we assume that…
Saddle point optimization is a critical problem employed in numerous real-world applications, including portfolio optimization, generative adversarial networks, and robotics. It has been extensively studied in cases where the objective…
Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error…
Nonconvex optimization problems such as the ones in training deep neural networks suffer from a phenomenon called saddle point proliferation. This means that there are a vast number of high error saddle points present in the loss function.…
A distributed nonsmooth robust resource allocation problem with cardinality constrained uncertainty is investigated in this paper. The global objective is consisted of local objectives, which are convex but nonsmooth. Each agent is…
The magnetostatic field distribution in a nonlinear medium amounts to the unique minimizer of the magnetic coenergy over all fields that can be generated by the same current. This is a nonlinear saddlepoint problem whose numerical solution…
The paper is devoted to the existence of weak Pareto solutions and the weak sharp minima at infinity property for a general class of constrained nonconvex vector optimization problems with unbounded constraint set via asymptotic cones and…
The main goal of this paper is to relate the topologically relevant stationary points of a cardinality-constrained optimization problem and its continuous reformulation up to their type. For that, we focus on the nondegenerate M- and…
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…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
The optimal allocation of resources for maximizing influence, spread of information or coverage, has gained attention in the past years, in particular in machine learning and data mining. But in applications, the parameters of the problem…
Motivated by a class of applied problems arising from physical layer based security in a digital communication system, in particular, by a secrecy sum-rate maximization problem, this paper studies a nonsmooth, difference-of-convex (dc)…
Rank and cardinality penalties are hard to handle in optimization frameworks due to non-convexity and discontinuity. Strong approximations have been a subject of intense study and numerous formulations have been proposed. Most of these can…
The cardinality-constrained mean-variance portfolio problem has garnered significant attention within contemporary finance due to its potential for achieving low risk while effectively managing risks and transaction costs. Instead of…