Double smoothing technique for infinite-dimensional optimization problems with applications to Optimal Control.

Categories Convex Optimization, Infinite Dimensional Optimization Tags , , , ,

In this paper, we propose an efficient technique for solving some infinite-dimensional problems over the sets of functions of time. In our problem, besides the convex point-wise constraints on state variables, we have convex coupling constraints with finite-dimensional image. Hence, we can formulate a finite-dimensional dual problem, which can be solved by efficient gradient methods. … Read more

Optimality conditions for various efficient solutions involving coderivatives: from set-valued optimization problems to set-valued equilibrium problems

Categories Complementarity and Variational Inequalities, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , , , , , , , , , , ,

We present a new approach to the study of a set-valued equilibrium problem (for short, SEP) through the study of a set-valued optimization problem with a geometric constraint (for short, SOP) based on an equivalence between solutions of these problems. As illustrations, we adapt to SEP enhanced notions of relative Pareto efficient solutions introduced in … Read more

The state-of-the-art in conic optimization software

Categories Linear, Cone and Semidefinite Programming, Optimization Software Benchmark Tags , ,

This work gives an overview over the major codes available for the solution of linear semidefinite (SDP) and second-order cone (SOCP) programs. Some developments since the 7th DIMACS Challenge [9, 17] are pointed out as well as some currently under way. Instead of presenting per- formance tables, reference is made to the ongoing benchmark [19] … Read more

A Linearly Convergent Algorithm for Solving a Class of Nonconvex/Affine Feasibility Problems

Categories Nonlinear Optimization Tags , , , , , , , ,

We introduce a class of nonconvex/affine feasibility problems, called (NCF), that consists of finding a point in the intersection of affine constraints with a nonconvex closed set. This class captures some interesting fundamental and NP hard problems arising in various application areas such as sparse recovery of signals and affine rank minimization that we briefly … Read more

On semidefinite programming relaxations of maximum k-section

Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization, Semi-definite Programming Tags , , ,

We derive a new semidefinite programming bound for the maximum k-section problem. For k=2 (i.e. for maximum bisection), the new bound is least as strong as the well-known bound by Frieze and Jerrum [A. Frieze and M. Jerrum. Improved Approximation Algorithms for MAX k-CUT and MAX BISECTION. Algorithmica, 18(1): 67-81, 1997]. For k > 2 … Read more

Relaxations of combinatorial problems via association schemes

Categories Combinatorial Optimization, Semi-definite Programming Tags ,

In this chapter we study a class of semidefinite programming relaxations of combinatorial problems. These relaxations are derived using the theory of coherent configurations in algebraic combinatorics. CitationDraft version of a chapter for “Handbook on SDP II” (M. Anjos and J. Lasserre, eds.), Springer.ArticleDownload View PDF

A biased random-key genetic algorithm for road congestion minimization

Categories Combinatorial Optimization, Meta Heuristics, Transportation Tags , , , , , ,

One of the main goals in transportation planning is to achieve solutions for two classical problems, the traffic assignment and toll pricing problems. The traffic assignment problem aims to minimize total travel delay among all travelers. Based on data derived from the first problem, the toll pricing problem determines the set of tolls and corresponding … Read more

A parallel multi-population biased random-key genetic algorithm for a container loading problem

Categories Combinatorial Optimization, Meta Heuristics, Production and Logistics Tags , , , ,

This paper presents a multi-population biased random-key genetic algorithm (BRKGA) for the Single Container Loading Problem (CLP) where several rectangular boxes of different sizes are loaded into a single rectangular container. The approach uses a maximal-space representation to manage the free spaces in the container. The proposed algorithm hybridizes a novel placement procedure with a … Read more

On the Safety First portfolio selection

Categories Finance and Economics, Stochastic Programming Tags , , , ,

A.D.Roy’s (1952) safety first (SF) approach to a financial portfolio selection is improved. Safety first means minimization of probability of poor returns. Improvement concerns a better estimation of the poor return probabilities by means of shortfall risk functions. Optimal SF-portfolio is sought similar to Roy’s geometric method but with a different efficient frontier. In case … Read more

Efficient preconditioner updates for shifted linear systems

Categories Nonlinear Systems and Least-Squares Tags , ,

We present a new technique for building effective and low cost preconditioners for sequences of shifted linear systems (A+aI)x=b, where A is symmetric positive definite and a>0. This technique updates a preconditioner for A, available in the form of an LDL’ factorization, by modifying only the nonzero entries of the L factor in such a … Read more