Related papers: A first-order multigrid method for bound-constrain…

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…

It is well known that multigrid methods are optimally efficient for solution of elliptic equations (O(N)), which means that effort is proportional to the number of points at which the solution is evaluated). Thus this is an ideal method to…

We introduce a first order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the homogeneous self-dual embedding, an equivalent…

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 focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…

A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points. First-order methods often get stuck at saddle points, greatly deteriorating their performance. Typically, to escape from…

We consider stochastic convex optimization with a strongly convex (but not necessarily smooth) objective. We give an algorithm which performs only gradient updates with optimal rate of convergence.

Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…

In the present paper we concentrate on an important issue in constructing a good multigrid solver: the choice of an efficient smoother. We will introduce all-at-once multigrid solvers for optimal control problems which show robust…

Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…

In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…

We show that the optimal complexity of Nesterov's smooth first-order optimization algorithm is preserved when the gradient is only computed up to a small, uniformly bounded error. In applications of this method to semidefinite programs,…

The filtering-clustering models, including trend filtering and convex clustering, have become an important source of ideas and modeling tools in machine learning and related fields. The statistical guarantee of optimal solutions in these…

In this paper we present a one dimensional second order accurate method to solve Elliptic equations with discontinuous coefficients on an arbitrary interface. Second order accuracy for the first derivative is obtained as well. The method is…

We consider finite Markov decision processes (MDPs) with convex constraints and known dynamics. In principle, this problem is amenable to off-the-shelf convex optimization solvers, but typically this approach suffers from poor scalability.…

We consider feasibility and constrained optimization problems defined over smooth and/or strongly convex sets. These notions mirror their popular function counterparts but are much less explored in the first-order optimization literature.…

We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…

We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…

We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…

In the development of first-order methods for smooth (resp., composite) convex optimization problems, where smooth functions with Lipschitz continuous gradients are minimized, the gradient (resp., gradient mapping) norm becomes a…