Global algorithm for solving linear multiplicative programming problems

Output-Space Branch-and-Bound Reduction Algorithm for a Class of Linear Multiplicative Programs

“…In this subsection, we give several exact examples to illustrate that the algorithm OSBBRA is effective and feasible. Example 1 [23,25,26,42] min…”

“…It can be seen that the calculation results of this algorithm are the same as those of BARON, but the running time of CPU used in our algorithm is less than that of BARON, especially the number of iterations used by BARON in solving Example 8 is much higher than that of algorithm OSBBRA. [26] (1.3148, 0.1396, 0.0, 0.4233) 0.8902 1 0.0601 10 −6 [39] (1.3148, 0.1396, 0.0000, 0.4233) 0.890190 3 0.047 0.05 [42] ( 8 BARON (1.0000, 1.9999, 1.0000, 1.0000, 1.0000) 9503.9999 155 1.4662 10 −6 OSBBRA (1.0000, 2.0000, 1.0000, 1.0000, 1.0000) 9503.9999 2 0.0691 10 −6…”

Global Algorithm for Generalized Affine Multiplicative Programming Problem

“…Example 9 (Shen and Huang [31]; Wang et al [15]). Example 10 (Shen and Huang [31]; Wang et al [15]).…”

“…In last two decades, many algorithms have been proposed for globally solving the problem (GAMP) and its special cases. According to characteristics of these algorithms, these algorithms can be mainly classified into parametric simplex algorithm [8], parametric successive underestimation method [9], monotonic optimization approach [10], rectangular branch-and-bound algorithms [11]- [18], outcome space approaches [19]- [24], polynomial time approximation algorithms [25]- [27], optimal level set methods [28], [29], linear decomposition methods [30], [31], heuristic method [32], outer approximation algorithm [33], and so on. Moreover, most of these reviewed algorithms require that each affine function in the objective function must be positive.…”

An Effective Global Optimization Algorithm for Quadratic Programs with Quadratic Constraints

“…In the last several decades, many algorithms have been developed for globally solving the (QPWQC) and its special cases, such as branch-and-bound method [12,13], approximation approach [14], robust approach [15], branch-reduce-bound algorithm [16][17][18][19], geometric programming approach [20][21][22][23], and others. Except for the above approaches, some global optimization algorithms [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] for linear multiplicative programming problems and generalized linear fractional programming problems can be used to solve the quadratic programs with quadratic constraints (QPWQC) considered in this paper.…”