Asia-Pacific Journal of Operational Research

The authors demonstrated in earlier papers that a maximal predictability portfolio (MPP) using a dynamic strategy leads to a significantly better ex-post performance than the one based on a static strategy and the index. In this paper, we will consider a maximal predictability portfolio subject to transaction cost. To reduce transaction cost, we employ turnover constraint. It will be shown that this approach leads to a significantly better performance than the standard MPP and the index.

Based on the convergent sequence of SDP relaxations for a multivariate polynomial optimization problem (POP) by Lasserre (2006), Waki et al. (2006) constructed a sequence of sparse SDP relaxations to solve sparse POPs efficiently. Nevertheless, the size of the sparse SDP relaxation is the major obstacle in order to solve POPs of higher degree. This paper proposes an approach to transform general POPs to quadratic optimization problems (QOPs), which allows to reduce the size of the SDP relaxation substantially. We introduce different heuristics resulting in equivalent QOPs and show how sparsity of a POP is maintained under the transformation procedure. As the most important issue, we discuss how to increase the quality of the SDP relaxation for a QOP. Moreover, we increase the accuracy of the solution of the SDP relaxation by applying additional local optimization techniques. Finally, we demonstrate the high potential of this approach through numerical results for large scale POPs of higher degree.

Earth mover's distance (EMD for short) is a perceptually meaningful dissimilarity measure between histograms. The computation of EMD reduces to a network flow optimization problem; however, it lays a heavy computational burden when the number of locations of histograms is large. In this paper, we address an efficient formulation for computing the exact EMD value. We prove that the EMD problem reduces to a problem with half the number of constraints regardless of the ground distance. We then propose a further reduced formula in which the number of variables is reduced from O(m²) to O(m) for histograms with m locations when the ground distance is derived from a graph with a homogeneous neighborhood structure. Specifically, EMD problems with L₁, L_∞ and D-norm ground distances can be reduced in this manner. Some experiments show that the reduction helps compute the EMD efficiently.

In this paper we present a new globalization strategy of the Barzilai-Borwein gradient method for large scale unconstrained optimization. Based on the filter technique introduced by Fletcher and Leyffer, a modified Barzilai-Borwein method is presented. We prove the global convergence of this method. Extensive numerical results on a set of CUTEr test problems show that the proposed method is competitive.

In this paper, we consider the projected gradient algorithms for solving the quadratic program with bound constraints and a single linear equality constraint (SLBQP). We establish the relationship between the Lagrangian multiplier in the projection subproblem and the Lagrangian multiplier in the original optimization problem. Then we give an improved initial estimate of the Lagrangian multiplier in the subproblem based on this relationship. It appears that this initial estimate is very close to the optimal Lagrangian multiplier after several iterations of the outer loop. This will reduce at most 40% of the computing time in the projection subproblem. This initial guess can also be used in all kinds of projected gradient methods for solving the SLBQP problem. The numerical results show that it brings much more improvement in monotone algorithms than in nonmonotone algorithms. We also apply the adaptive steepest descent step-size and the Dai-Yuan step-size which are two monotone step-sizes to the projected gradient method of this SLBQP problem. Our numerical experiments showed that their performance can be better than some other monotone projected gradient methods.

A new method of moving asymptotes for large scale minimization subject to linear inequality constraints is discussed in this paper. In each step of the iterative process, a descend direction is obtained by solving a convex separable subproblem with dual technique. The new rules for controlling the asymptotes parameters are designed by the trust region radius and some approximation properties such that the global convergence of the new method are obtained. The numerical results show that the new method may be capable of processing some large scale problems.

In this paper we apply the well known sample average approximation (SAA) method to solve a class of stochastic variational inequality problems (SVIPs). We investigate the existence and convergence of a solution to the sample average approximated SVIP. Under some moderate conditions, we show that the sample average approximated SVIP has a solution with probability one and with probability approaching one exponentially fast with the increase of sample size, the solution converges to its true counterpart. Finally, we apply the existence and convergence results to SAA method for solving a class of stochastic nonlinear complementarity problems and stochastic programs with stochastic constraints.

We evaluate the Arrows Classification Method (ACM) for grouping objects based on the similarity of their data. This is a new method, which aims to achieve a balance between the conflicting objectives of maximizing internal cohesion and external isolation in the output groups. The method is widely applicable, especially in simulation input and output modelling, and has previously been used for grouping machines on an assembly line, based on data on time-to-repair; and hospital procedures, based on length-of-stay data. The similarity of the data from a pair of objects is measured using the two-sample Cramér-von-Mises goodness of fit statistic, with bootstrapping employed to find the significance or p-value of the calculated statistic. The p-values coming from the paired comparisons serve as inputs to the ACM, and allow the objects to be classified such that no pair of objects that are grouped together have significantly different data. In this article, we give the technical details of the method and evaluate its use through testing with specially generated samples. We will also demonstrate its practical application with two real examples.