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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…

We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…

Several ways to accelerate the solution of 2D/3D linear min-max problems in $n$ constraints are discussed. We also present an algorithm for solving such problems in the 2D case, which is superior to CGAL's linear programming solver, both in…

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…

We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are…

There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…

In this paper, we consider the problem of scheduling an application on a parallel computational platform. The application is a particular task graph, either a linear chain of tasks, or a set of independent tasks. The platform is made of…

This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…

Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…

Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…

We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection' of a…

Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…

In this paper, we give an algorithm that finds an epsilon-approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer…

In this paper, we prove that the Max-Morse Matching Problem is approximable, thus resolving an open problem posed by Joswig and Pfetsch. We describe two different approximation algorithms for the Max-Morse Matching Problem. For…

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…

This article presents a new and efficient alternative to well established algorithms for molecular geometry optimization. The new approach exploits the approximate decoupling of molecular energetics in a curvilinear internal coordinate…

This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of…

We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of…

In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…

We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with…