One-step algorithms are presented for two classes of structured stochastic games, namely, those with additive rewards and transitions and those which have switching controllers. Solutions to such classes of games unde...
详细信息
One-step algorithms are presented for two classes of structured stochastic games, namely, those with additive rewards and transitions and those which have switching controllers. Solutions to such classes of games under the average reward criterion can be derived from optimal solutions to appropriate bilinear programs. The validity of using bilinear programming as a solution method follows from two preliminary theorems, the first of which is a complete classification of undiscounted stochastic games with optimal stationary strategies. The second of these preliminary theorems relaxes the conditions of the classification theorem for certain classes of stochastic games and provides the basis for the bilinear programming results. Analogous results hold for the discounted stochastic games with the above special structures.
This paper is concerned with a new approach for solving quadratic assignment problems (QAP). We first reformulate QAP as a concave quadratic programming problem and apply an outer approximation algorithm. In addition,...
详细信息
This paper is concerned with a new approach for solving quadratic assignment problems (QAP). We first reformulate QAP as a concave quadratic programming problem and apply an outer approximation algorithm. In addition, an improvement routine is incorporated in the final stage of the algorithm. Computational experiments on a set of standard data demonstrate that this algorithm can yield favorable results with a relatively low computational effort.
A new design method of PID structured controllers to achieve robust performance is developed. Both robust stabilization and performance conditions are losslessly expressed by bilinear constraints in the proportional-d...
详细信息
A new design method of PID structured controllers to achieve robust performance is developed. Both robust stabilization and performance conditions are losslessly expressed by bilinear constraints in the proportional-double derivative variable. (k(P);k(DD)) and the integral-derivative variable. (k(I);k(D)). Therefore, the considered control design can be efficiently solved by alternating optimization between. (k(P);k(DD)) and (k(I);k(D)), which is a 2D computationally tractable program. The proposed method works equally efficiently whenever even higher order differential or integral terms are included in PID control to improve its robustness and performance. Numerical examples are provided to show the viability of the proposed development. Copyright (C) 2016 John Wiley & Sons, Ltd.
In this paper, we consider the Mixed-Integer bilinear programming problem, a widely-used reformulation of the classical mixed-integer quadratic programming problem. For this problem we describe a branch and -cut algor...
详细信息
In this paper, we consider the Mixed-Integer bilinear programming problem, a widely-used reformulation of the classical mixed-integer quadratic programming problem. For this problem we describe a branch and -cut algorithm for its exact solution, based on a new family of intersection cuts derived from bilinearspecific disjunctions. We also introduce a new branching rule that is specifically designed for bilinear problems. We computationally analyze the behavior of the proposed algorithm on a large set of mixed-integer quadratic instances from the MINLPIib problem library. Our results show that our method, even without intersection cuts, is competitive with a state-of-the-art mixed-integer nonlinear solver. As to intersection cuts, their extensive use at each branching node tends to slow down the solver for most problems in our test bed, but they are extremely effective for some specific instances. (C) 2019 Elsevier B.V. All rights reserved.
The aim of this paper is to develop a new methodology for solving bimatrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs), which are called TIFN bimatrix games for short. In this methodology, we...
详细信息
The aim of this paper is to develop a new methodology for solving bimatrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs), which are called TIFN bimatrix games for short. In this methodology, we define the concepts of the value-index and ambiguity-index and hereby develop a difference-index based ranking method, which is proven to be a total order. The parameterized bilinear programming models are derived from a pair of auxiliary TIFN mathematical programming models, which are used to determine solutions of TIFN bimatrix games. Validity and applicability of the models and method proposed in this paper are illustrated with a practical example.
Traditional pivoting methods for solving the linear complementarity problem can only guarantee convergence for problems having well-defined structures. Recently, optimization methods based on linear, quadratic, and b...
详细信息
Traditional pivoting methods for solving the linear complementarity problem can only guarantee convergence for problems having well-defined structures. Recently, optimization methods based on linear, quadratic, and bilinear programming have been developed to broaden the class of problems that can be solved efficiently. Discussion is given to the strengths and weaknesses of each of the methods. The linear programming approach, proposed by Mangasarian, is the most efficient, once an appropriate objective function is found. The quadratic programming methods discussed are limited to specialized procedures for the complementarity problem. One, proposed by Cheng, is based on the Levitin-Poljak gradient projection method, while another, credited to Cirina, is based on Karush-Kuhn-Tucker theory. Both are successful only on some problems. The 2 bilinear programming algorithms examined are the most general. For any problem, they are assured to find at least one solution or conclude that none exists.
It is understood that the Hilbert transform pairs of orthonormal wavelet bases can only be realized approximately by the scaling filters of conjugate quadrature filter (CQF) banks. In this paper, the approximate FIR r...
详细信息
It is understood that the Hilbert transform pairs of orthonormal wavelet bases can only be realized approximately by the scaling filters of conjugate quadrature filter (CQF) banks. In this paper, the approximate FIR realization of the Hilbert transform pairs is formulated as an optimization problem in the sense of the l(p) (p = 1, 2, or infinite) norm minimization on the approximate error of the magnitude and phase conditions of the scaling filters. The orthogonality and regularity conditions of the CQF bank pairs are taken as the constraints of such an optimization problem. Whereafter the branch and bound technique is employed to obtain the globally optimal solution of the resulting bilinear program optimization problem. Since the orthogonality and regularity conditions are explicitly taken as the constraints of our optimization problem, the attained solution is an approximate Hilbert transform pair satisfying these conditions exactly. Some orthogonal wavelet bases designed herein demonstrate that our design scheme is superior to those that have been reported in the literature. Moreover, the designed orthogonal wavelet bases show that minimizing the norm of the approximate error should be advocated for obtaining better approximated Hilbert pairs.
We propose a vector optimization approach to linear Cournot oligopolistic market equilibrium models where the strategy sets depend on each other. We use scalarization technique to find a Pareto efficient solution to t...
详细信息
We propose a vector optimization approach to linear Cournot oligopolistic market equilibrium models where the strategy sets depend on each other. We use scalarization technique to find a Pareto efficient solution to the model by using a jointly constrained bilinear programming formulation. We then propose a decomposition branch-and-bound algorithm for globally solving the resulting bilinear problem. The subdivision takes place in one-dimensional intervals that enables solving the problem with relatively large sizes. Numerical experiments and results on randomly generated data show the efficiency of the proposed algorithm.
We propose a finitely terminating primal-dual bilinear programming algorithm for the solution of the NP-hard absolute value equation (AVE): Ax -vertical bar x vertical bar = b, where A is an n x n square matrix. The a...
详细信息
We propose a finitely terminating primal-dual bilinear programming algorithm for the solution of the NP-hard absolute value equation (AVE): Ax -vertical bar x vertical bar = b, where A is an n x n square matrix. The algorithm, which makes no assumptions on AVE other than solvability, consists of a finite number of linear programs terminating at a solution of the AVE or at a stationary point of the bilinear program. The proposed algorithm was tested on 500 consecutively generated random instances of the AVE with n = 10, 50, 100, 500 and 1,000. The algorithm solved 88.6% of the test problems to an accuracy of 10(-6).
This paper presents two linear cutting plane algorithms that refine existing methods for solving disjoint bilinear programs. The main idea is to avoid constructing (expensive) disjunctive facial cuts and to accelerate...
详细信息
This paper presents two linear cutting plane algorithms that refine existing methods for solving disjoint bilinear programs. The main idea is to avoid constructing (expensive) disjunctive facial cuts and to accelerate convergence through a tighter bounding scheme. These linear programming based cutting plane methods search the extreme points and cut off each one found until an exhaustive process concludes that the global minimizer is in hand. In this paper, a lower bounding step is proposed that serves to effectively fathom the remaining feasible region as not containing a global solution, thereby accelerating convergence. This is accomplished by minimizing the convex envelope of the bilinear objective over the feasible region remaining after introduction of cuts. Computational experiments demonstrate that augmenting existing methods by this simple linear programming step is surprisingly effective at identifying global solutions early by recognizing that the remaining region cannot contain an optimal solution. Numerical results for test problems from both the literature and an application area are reported.
暂无评论