Related papers: A Linear Scalarization Proximal Point Method for Q…
In this short survey, I revisit the role of the proximal point method in large scale optimization. I focus on three recent examples: a proximally guided subgradient method for weakly convex stochastic approximation, the prox-linear…
We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal…
We revisit the smooth convex-concave bilinearly-coupled saddle-point problem of the form $\min_x\max_y f(x) + \langle y,\mathbf{B} x\rangle - g(y)$. In the highly specific case where each of the functions $f(x)$ and $g(y)$ is either affine…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…
We give in this paper a convergence result concerning parallel synchronous algorithm for nonlinear fixed point problems with respect to the euclidian norm in $\Rn$. We then apply this result to some problems related to convex analysis like…
In multi-objective optimization, minimizing the worst objective can be preferable to minimizing the average objective, as this ensures improved fairness across objectives. Due to the non-smooth nature of the resultant min-max optimization…
This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
We define quasiconvex programming, a form of generalized linear programming in which one seeks the point minimizing the pointwise maximum of a collection of quasiconvex functions. We survey algorithms for solving quasiconvex programs either…
Trace norm regularization is a widely used approach for learning low rank matrices. A standard optimization strategy is based on formulating the problem as one of low rank matrix factorization which, however, leads to a non-convex problem.…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…
This paper presents a novel approach to solving large-scale minimax problems with nonsmooth regularizers. We propose a stochastic implicit proximal point algorithm with variance reduction techniques where stochastic oracles are selected in…
This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying…
Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…
We propose an algorithm to generate inner and outer polyhedral approximations to the upper image of a bounded convex vector optimization problem. It is an outer approximation algorithm and is based on solving norm-minimizing scalarizations.…
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but…
This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending…