相关论文: Sublinear Scalarizations for Proper and Approximat…

We present a provably more efficient implementation of the Minimum Norm Point Algorithm conceived by Fujishige than the one presented in \cite{FUJI06}. The algorithm solves the minimization problem for a class of functions known as…

In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…

This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…

We consider the problem of noiseless and noisy low-rank tensor completion from a set of random linear measurements. In our derivations, we assume that the entries of the tensor belong to a finite field of arbitrary size and that…

We propose an algorithm that produces a non-decreasing sequence of subsolutions for a class of optimal control problems distinguished by the property that the associated Bellman operators preserve convexity. In addition to a theoretical…

In this paper, approximate optimality conditions and sensitivity analysis in nearly convex optimization are discussed. More precisely, as in the spirit of convex analysis, we introduce the concept of $\varepsilon$-subdifferential for nearly…

We consider the minimization of non-convex quadratic forms regularized by a cubic term, which exhibit multiple saddle points and poor local minima. Nonetheless, we prove that, under mild assumptions, gradient descent approximates the…

Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…

We provide a simple and flexible framework for designing differentially private algorithms to find approximate stationary points of non-convex loss functions. Our framework is based on using a private approximate risk minimizer to "warm…

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…

This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…

We consider distributed convex optimization problems that involve a separable objective function and nontrivial functional constraints, such as Linear Matrix Inequalities (LMIs). We propose a decentralized and computationally inexpensive…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…

In this paper we introduce two conceptual algorithms for minimising abstract convex functions. Both algorithms rely on solving a proximal-type subproblem with an abstract Bregman distance based proximal term. We prove their convergence when…

This paper defines a convertible nonconvex function(CN function for short) and a weak (strong) uniform (decomposable, exact) CN function, proves the optimization conditions for their global solutions and proposes algorithms for solving the…

We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate…

We show that the graph of a bent function is a Salem set in an appropriate sense. We also establish a simple result that quantifies redundancies in the difference operators of a function, which applies to bent functions over fields of odd…

The use of min-max optimization in adversarial training of deep neural network classifiers and training of generative adversarial networks has motivated the study of nonconvex-nonconcave optimization objectives, which frequently arise in…

In this paper, we discuss scalar Lagrangian multipliers and vector Lagrangian multipliers for constrained set-valued optimization problems. We obtain some necessary conditions, sufficient conditions, as well as necessary and sufficient…