Very hard optimization problems, i.e., problems with a large number of variables and local minima, have been effectively attacked with algorithms which mix local searches with heuristic procedures in order to widely explore the search space. A Population Based Approach based on a Monotonic Basin Hopping optimization algorithm has turned out to be very effective … Read more
We present semidefinite relaxations of nonconvex, box-constrained quadratic programming, which incorporate the first- and second-order necessary optimality conditions. We compare these relaxations with a basic semidefinite relaxation due to Shor, particularly in the context of branch-and-bound to determine a global optimal solution, where it is shown empirically that the new relaxations are significantly stronger. We … Read more
We describe a major update of our Matlab freeware GloptiPoly for parsing generalized problems of moments and solving them numerically with semidefinite programming. Citation 28 June 2007 Article Download View GloptiPoly 3: moments, optimization and semidefinite programming
In this paper, we propose lifting techniques for generating strong cuts for nonlinear programs that are globally-valid. The theory is geometric and provides intuition into lifting-based cut generation procedures. As a special case, we find short proofs of earlier results on lifting techniques for mixed-integer programs. Using convex extensions, we obtain conditions that allow sequence-independent … Read more
In this paper, simple linear programming procedure is proposed for generating all efficient extreme points and all efficient extreme rays of a multiple objective linear programming problem (V P). As an application we solve the linear multiplicative programming associated with the problem (VP). Citation submitted Article Download View Generating All Efficient Extreme Points in Multiple … Read more
It is shown that, contrary to a claim of [D. E. Finkel, and C. T. Kelley, Additive scaling and the DIRECT algorithm, J. Glob. Optim. 36 (2006) 597-608], it is possible to divide the smallest hypercube which contains the low function value by considering hyperrectangles whose points are located on the diagonal of the center … Read more
We consider the problem of locating a single radiating source from several noisy measurements using a maximum likelihood (ML) criteria. The resulting optimization problem is nonconvex and nonsmooth and thus finding its global solution is in principal a hard task. Exploiting the special structure of the objective function, we introduce and analyze two iterative schemes … Read more
This paper presents an outcome-space outer approximation algorithm for globally solving the linear multiplicative programming problem. We prove that the proposed algorithm is finite. To illustrate the new algorithm, we apply it to solve some sample problems. Citation 10, Hanoi University of Technology, 07/2007 Article Download View Outcome-Space Outer Approximation Algorithm for Linear Multiplicative Programming
We present three new stopping rules for Multistart based methods. The first uses a device that enables the determination of the coverage of the bounded search domain. The second is based on the comparison of asymptotic expectation values of observable quantities to the actually measured ones. The third offers a probabilistic estimate for the number … Read more
Yu and Liu’s strong duality theorem under the time-sharing property requires the Slater condition to hold for the considered general nonconvex problem, what is satisfied for the specific application. We further extend the scope of the theorem under Ky Fan convexity which is slightly weaker than Yu&Lui’s time-sharing property. Article Download View Comments on "Dual … Read more