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
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
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
The main goal of this paper is to develop uniformly optimal first-order methods for large-scale convex programming (CP). By uniform optimality we mean that the first-order methods themselves do not require the input of any problem parameters, but can still achieve the best possible iteration complexity bounds. To this end, we provide a substantial generalization … 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
The main goal of this paper is to develop uniformly optimal first-order methods for large-scale convex programming (CP). By uniform optimality we mean that the first-order methods themselves do not require the input of any problem parameters, but can still achieve the best possible iteration complexity bounds. To this end, we provide a substantial generalization … Read more
This paper presents a local search, based on a new neighborhood for the job-shop scheduling problem, and its application within a biased random-key genetic algorithm. Schedules are constructed by decoding the chromosome supplied by the genetic algorithm with a procedure that generates active schedules. After an initial schedule is obtained, a local search heuristic, based … Read more
This paper presents a local search, based on a new neighborhood for the job-shop scheduling problem, and its application within a biased random-key genetic algorithm. Schedules are constructed by decoding the chromosome supplied by the genetic algorithm with a procedure that generates active schedules. After an initial schedule is obtained, a local search heuristic, based … Read more
We present a scalable approach and implementation for solving stochastic programming problems, with application to the optimization of complex energy systems under uncertainty. Stochastic programming is used to make decisions in the present while incorporating a model of uncertainty about future events (scenarios). These problems present serious computational difficulties as the number of scenarios becomes … Read more