Search

This paper presents a novel range division and contraction approach for globally solving nonconvex quadratic program with quadratic constraints. By constructing new underestimating linear relaxation functions, we can transform the initial nonconvex quadratic program problem into a linear program relaxation problem. By employing a branch and bound scheme with a range contraction approach, we describe a novel global optimization algorithm for effectively solving nonconvex quadratic program with quadratic constraints. Finally, the global convergence of the proposed algorithm is proved and numerical experimental results demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a deterministic global optimization algorithm for solving minimax linear fractional programming (MLFP). In this algorithm, a new linearization technique is proposed, which uses more information of the objective function of the (MLFP) than other techniques. By utilizing this new linearization technique, the initial nonconvex programming problem (MLFP) is reduced to a sequence of linear relaxation programming (LRP) problems, which can provide reliable lower bound of the optimal value. The proposed algorithm is convergent to the global minimum of the (MLFP) through the successive refinement of the feasible region and solutions of a series of the (LRP). Compared with the known algorithms, numerical results show that the proposed algorithm is robust and effective. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, a global optimization algorithm is proposed for solving sum of generalized polynomial ratios problem (P) which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solve the problem (P). For such problems, we present a branch and bound algorithm. In this method, by utilizing exponent transformation and new three-level linear relaxation method, a sequence of linear relaxation programming of the initial nonconvex programming problem (P) are derived which are embedded in a branch and bound algorithm. The proposed method need not introduce new variables and constraints and it is convergent to the global minimum of prime problem by means of the subsequent solutions of a series of linear programming problems. Several numerical examples in the literatures are tested to demonstrate that the proposed algorithm can systematically solve these examples to find the approximate ϵ-global optimum. [Copyright &y& Elsevier]

Abstract: A branch and bound algorithm is proposed for globally solving a class of nonconvex programming problems (NP). For minimizing the problem, linear lower bounding functions (LLBFs) of objective function and constraint functions are constructed, then a relaxation linear programming is obtained which is solved by the simplex method and which provides the lower bound of the optimal value. The proposed algorithm is convergent to the global minimum through the successive refinement of linear relaxation of the feasible region and the solutions of a series of linear programming problems. And finally the numerical experiment is reported to show the feasibility and effectiveness of the proposed algorithm. [Copyright &y& Elsevier]