Related papers: Solution uniqueness of convex optimization problem…

Using an optimization algorithm to solve a machine learning problem is one of mainstreams in the field of science. In this work, we demonstrate a comprehensive comparison of some state-of-the-art first-order optimization algorithms for…

Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…

We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…

We consider a compound testing problem within the Gaussian sequence model in which the null and alternative are specified by a pair of closed, convex cones. Such cone testing problem arise in various applications, including detection of…

We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…

A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added…

Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions;…

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…

The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…

Training neural networks involves solving large-scale non-convex optimization problems. This task has long been believed to be extremely difficult, with fear of local minima and other obstacles motivating a variety of schemes to improve…

This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical…

Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…

In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

In this paper we prove the uniqueness and radial symmetry of minimizers for variational problems that model several phenomena. The uniqueness is a consequence of the convexity of the functional. The main technique is Fourier transform of…

In this paper, we study two classes of optimal reinsurance models from perspectives of both insurers and reinsurers by minimizing their convex combination where the risk is measured by a distortion risk measure and the premium is given by a…

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…

Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting…

Convex optimization encompasses a wide range of optimization problems that contain many efficiently solvable subclasses. Interior point methods are currently the state-of-the-art approach for solving such problems, particularly effective…

The common task in matrix completion (MC) and robust principle component analysis (RPCA) is to recover a low-rank matrix from a given data matrix. These problems gained great attention from various areas in applied sciences recently,…