A cutting-plane procedure for integer programming (IP) problems usually involves invoking a black-box procedure (such as the Gomory-Chvatal (GC) procedure) to compute a cutting-plane. In this paper, we describe an alternative paradigm of using the same cutting-plane black-box. This involves two steps. In the first step, we design an inequality cx = d + 1\} … Read more
This is a progress report on an implementation of the active-set method for nonlinear programming proposed in [6] that employs piecewise linear models in the active-set prediction phase. The motivation for this work is to develop an algorithm that is capable of solving large-scale problems, including those with a large reduced space. Unlike SQP methods, … Read more
We propose new versions of accelerated first order methods for convex composite optimization, where the prox parameter is allowed to increase from one iteration to the next. In particular we show that a full backtracking strategy can be used within the FISTA \cite{Beck-Teboulle-2009} and FALM algorithms \cite{Goldfarb-Ma-Scheinberg-2010} while preserving their worst-case iteration complexities of $O(\sqrt{L(f)/\epsilon})$. … Read more
The low-rank matrix recovery (LMR) arises in many fields such as signal and image processing, statistics, computer vision, system identification and control, and it is NP-hard. It is known that under some restricted isometry property (RIP) conditions we can obtain the exact low-rank matrix solution by solving its convex relaxation, the nuclear norm minimization. In … Read more
The electrical vehicle energy management can be expressed as a Bang-Bang optimal control problem. In this work, we discuss on a new formulation and about the way to approximate this optimal control problem of Bang-Bang type via a discretization technique associated with a Branch-and-Bound algorithm. The problem that we focus on, is the minimization of … Read more
We present a first order approach for solving semidefinite programs. Goal of this approach is to compute a solution of the SDP up to high accuracy in spite of using only partial second order information. We propose a hybrid approach that uses an accelerated projection method to generate an approximate solution and then switches to … Read more
The electrical vehicle energy management can be expressed as a Bang-Bang optimal control problem. In this work, we discuss on a new formulation and about the way to approximate this optimal control problem of Bang-Bang type via a discretization technique associated with a Branch-and-Bound algorithm. The problem that we focus on, is the minimization of … Read more
The recent approach of solving large scale semidefinite programs with a first order method by minimizing an augmented primal-dual function is extended to doubly nonnegative programs. Regularity of the augmented primal-dual function is established under the condition of uniqueness and strict complementarity. The application to the doubly nonnegative cone is motivated by the fact that … Read more
In their 1972 paper ‘How good is the simplex algorithm ?’ Klee and Minty present a class of problems the simplex algorithm for linear programming (LP) is not able to solve in a polynomial way. Later developments have resulted in algorithms by Khachiyan and Karmarkar that do solve LP in a polynomial way, although the … Read more
In this paper, we study a class of biquadratic optimization problems. We first relax the original problem to its semidefinite programming (SDP) problem and discuss the approximation ratio between them. Under some conditions, we show that the relaxed problem is tight. Then we consider how to approximately solve the problems in polynomial time. Under several … Read more