Search

In this article, we present a parametric linear relaxation algorithm for globally solving the nonconvex quadratic programming (NQP). In this algorithm, a new parametric linearized technique is proposed for generating parametric linear relaxation programming (PLRP) of the NQP, which can be used to determine the lower bound of global minimum value of the NQP. To improve the convergent speed of the proposed algorithm, a pruning operation is employed to compress the investigated region. By subdividing subsequently the initial domain and solving subsequently a series of parametric linear relaxation programming problems over the subdivided domain, the proposed algorithm is convergent to the global minimum of the NQP. Finally, an engineering problem for the design of heat exchanger network and some test examples are used to verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this technical note, we give a short extension application for a deterministic global optimization algorithm proposed in [Y. Ji, K.-C. Zhang, S.-J. Qu, A deterministic global optimization algorithm, Applied Mathematics and Computation 185 (2007) 382–387]. Actually our result is slightly more general, since it does not impose any special sign restrictions on numerators and denominators of the ratios. The only assumption is that the denominators of the ratios are nonzero over the feasible region of the problem. For clarity we use the same notations for the different equivalent problems and the corresponding relaxation linear programming (RLP) as done in Ji et al. (2007). [Copyright &y& Elsevier]

Abstract: Generalized geometric programming (GGP) problem occurs frequently in engineering design and management. In this paper, a branch-and-pruning global optimization algorithm is proposed for GGP. By utilizing some transformations, a linear relaxation of the problem (GGP) is obtained based on the linear lower bound functions of objective and constraint functions inside some hyperrectangle region. Then a new pruning technique is given to accelerate the convergence of the given algorithm, and this pruning technique offers the possibility to cut away a large part of the current investigated region in which there no exist global optimum solution. The proposed algorithm which connects branch-and-bound method with the pruning technique successfully is convergent to the global minimum, according to the successive refinement of the linear relaxation of feasible region of the objective function and the solutions of a series of linear relaxation problems. And finally numerical experiment is given to illustrate the feasibility and efficiency of the proposed algorithm. [Copyright &y& Elsevier]