Search

This paper presents a branch-delete-bound algorithm for effectively solving the global minimum of quadratically constrained quadratic programs problem, which may be nonconvex. By utilizing the characteristics of quadratic function, we construct a new linearizing method, so that the quadratically constrained quadratic programs problem can be converted into a linear relaxed programs problem. Moreover, the established linear relaxed programs problem is embedded within a branch-and-bound framework without introducing any new variables and constrained functions, which can be easily solved by any effective linear programs algorithms. By subsequently solving a series of linear relaxed programs problems, the proposed algorithm can converge the global minimum of the initial quadratically constrained quadratic programs problem. Compared with the known methods, numerical results demonstrate that the proposed method has higher computational efficiency.

Hysteresis phenomenon of tensile load (stress) under extension and recovery processes were estimated in terms of time dependence of tensile load by using several kinds of knitted fabrics. The measurements were done under strip biaxial extension corresponding to uniaxial extension with a fixed dimension in the direction perpendicular to elongation. The present concept was based on tensile load (stress) relaxation in elongation and restricted sides. To attempt mathematical evaluation, a simple hypothesis described by hereditary integral was proposed to explain the hysteresis of tensile load (strain), strain routes under extension, and recovery processes, in which the extension and recovery routes were formulated as addition and subtraction of step function of strain history, respectively. The calculated curves were in good agreement with the experimental curves in the large deformation region. The theoretical calculation to give the best fit with experimental curve could be realized by using n adopted as an exponent to describe the "linearizing method" (F = Yen, where F is the tensile load and e is strain of a fabric) proposed by Kawabata et al. The present evaluation improved on their proposal, since the present theory can represent the hysteresis routes by using the same value of parameter n. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a deterministic global optimization algorithm for solving nonconvex quadratically constrained quadratic programs (NQP) is proposed. Utilizing a new linearizing method, the initial nonlinear and nonconvex NQP problem is reduced to a sequence of linear programming problems. The proposed algorithm is proven to be convergent to the global minimum through the solutions of a series of linear programming problems. Several NQP examples in the literatures are tested to demonstrate that the proposed method can systematically solve these examples to find the global optimum within a prespecified error. [Copyright &y& Elsevier]

Abstract: In this paper, we combine the new global optimization method proposed by Qu et al. [S.J. Qu, K.C. Zhang, Y. Ji, A global optimization algorithm using parametric linearization relaxation, Appl. Math. Comput. 186 (2007) 763–771] with a suitable deleting technique to propose a new accelerating global optimization algorithm for solving the non-convex quadratic optimization problems with non-convex quadratic constraints (NQP). This technique offers a possibility to cut away a large part of the currently investigated region in which the global optimal solution of NQP does not exist, and can be seen as an accelerating device for the global optimization algorithm of the NQP problems. Compared with the method in Qu et al. (2007), numerical results show that the computational efficiency is obviously improved by using this new technique in the number of iterations, the required list length and the overall execution time of the algorithm. [Copyright &y& Elsevier]

Abstract: In this paper a global optimization algorithm based on a parametric linearizing method for generalized quadratic programming (GQP), i.e., the quadratic programming problem with nonconvex quadratic constraints, is proposed. By utilizing the linearizing method initial nonconvex nonlinear problem GQP is reduced to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region and of the objective function. The proposed algorithm is convergent to the global minimum of GQP by means of the subsequent solutions of a series of linear programming problems. Test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve global minimum of GQP on a microcomputer. [Copyright &y& Elsevier]