Preconditioning by a conjugate projector is combined with the recently proposed MPRGP algorithm for the solution of bound constrained quadratic programming problems. If applied to the partially bound constrained problems, such as those arising from the application of FETI based domain decomposition methods to the discretized elliptic boundary variational inequalities, the resulting algorithm is...

In this paper, we describe a two-stage method for solving optimization problems with bound constraints. It combines the active-set estimate described in [1] with a modification of the nonmonotone line search framework recently proposed in [2]. In the first stage, the algorithm exploits a property of the active-set estimate that ensures a significant reduction of the objective function when sett...

A stochastic algorithm for global optimization subject to simple bounds is described. The method is applicable to black-box functions which may be non-smooth or discontinuous. The algorithm is in the spirit of the deterministic algorithm direct of Jones, Perttunen, and Stuckman. Like direct, it generates successively finer covers of the feasible region, where each cover consists of a finite num...

An algorithm for solving large nonlinear optimization problems with simple bounds is de scribed It is based on the gradient projection method and uses a limited memory BFGS matrix to approximate the Hessian of the objective function It is shown how to take advan tage of the form of the limited memory approximation to implement the algorithm e ciently The results of numerical tests on a set of l...

Abstract. In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. We define a linesearch-based solution method, and we show that it converges to a set of Pareto stationary points. To this aim, we carry out a theoretic...

In this paper, we consider the extension of multi-objective constraint optimization algorithms to the case where there are additional tradeoffs, reducing the number of optimal solutions. We focus especially on branch-and-bound algorithms which use a mini-buckets algorithm for generating the upper bound at each node (in the context of maximizing values of objectives). Since the main bottleneck o...

Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the Branch and Bound algorithm. Symmetry may induce large search trees with multiple equivalent solutions, i.e. with the same optimal value. Dealing with symmetry requires detecting and classifying it first. This paper develops several methods for ...

Global optimization subject to bound constraints helps answer many practical questions in chemistry, molecular biology, economics. Most of algorithms for solution of global optimization problems are a combination of interval methods and exhuastive search. The efficiency of such algorithms is characterized by their ability to detect and eliminate sub-optimal feasible regions. This ability is inc...