(1)申培萍,专著,《全局优化方法》,北京,科学出版社,2006年 (2)P Shen, W Li, X Bai, Maximizing for the sum of ratios of two convex functions over a convex set, Computers & Operations Research 40 (2013) 2301–2307 . (3)P Shen, X Li, Branch-reduction-bound algorithm for generalized geometric programming, Journal of Global Optimization 56 (2013) 1123–1142 . (4)P Shen, X Bai,Global optimization for generalized geometric programming problems with discrete variables, Optimization 62 ( 2013) 895–917 . (5)P Shen, Y Ma, Y Chen, Global optimization for the generalized polynomial sum of ratios problem, Journal of Global Optimization 50(3) (2011) 439-455 . (6)P Shen, L Jin,Using conical partition to globally maximizing the nonlinear sum of ratios,Applied Mathematical Modelling 34 (2010) 2396–2413 . (7)P Shen, Y Chen, Y Ma,A nonisolated optimal solution for special reverse convex programming problems,Journal of Computational and Applied Mathematics 224(2009) 219-229 . (8)P Shen, Y Duan, Y Pei, A simplicial branch and duality bound algorithm for the sum of convex–convex ratios problem, Journal of Computational and Applied Mathematics 223(2009) 145-158 . (9)P Shen, X Bai, W Li, A new accelerating method for globally solving a class of nonconvex programming problems, Nonlinear Analysis: Theory, Methods & Aplications 102(2009) 2866-2876 . (10)P Shen, X Li, H Jiao, Accelerating method of global optimization for signomial geometric programming, Journal of Computational and Applied Mathematics 214 (2008)66-77 . (11)P Shen, Y Ma, Y Chen, A robust algorithm for generalized geometric Programming, Journal of Global Optimization 41 (2008) 593-612 . (12) P Shen, C Wang, Global optimization for sum of generalized fractional functions, Journal of Computational and Applied Mathematics 214 (2008) 1-12 . (13) P Shen, G Yuan, Global optimization for the sum of generalized polynomial fractional functions, Mathematical Methods of Operations Research 65 (2007) 445-459 . (14) P Shen, H Jiao, A new rectangle branch-and-pruning approach for generalized geometric programming, Applied Mathematics and Computation 183 (2006) 1027–1038 . (15) P Shen, C Wang, Global optimization for sum of linear ratios problem with coefficients, Applied Mathematics and Computation 176 (2006) 219–229 . (16) P Shen, H Jiao, Linearization method for a class of multiplicative programming with exponent, Applied Mathematics and Computation 183 (2006) 328–336. (17)P Shen, W Li, Y Liang,Branch-reduction-bound algorithm for linear sum-of-ratios fractional programs, Pacific Journal of Optimization 11(1)(2015) 79-99, (18)P Shen, C Wang. Linear decomposition approach for a class of nonconvex programming problems. Journal of Inequalities and Applications 2017:74, DOI: 10.1186/s13660-017-1342-y. (19)P Shen, T Zhang, C Wang. Solving a class of generalized fractional programming problems using the feasibility of linear programs. Journal of Inequalities and Applications 2017:147, DOI 10.1186/s13660-017-1420-1. (20)X Yang, Y Zhang, H Liu & P Shen. A new second-order infeasible primal-dual path-following algorithm for symmetric optimization. Numerical Functional Analysis and Optimization 37(4) (2016) 499-519, DOI:10.1080/01630563.2016.1138127. (21)C Wang, Y Bai & P Shen. A practicable branch-and-bound algorithm for globally solving linear multiplicative programming, Optimization 66(3)(2017),397-405, DOI: 10.1080/02331934.2016.1269765 (22)P Shen, T Lu. Regional division and reduction algorithm for minimizing the sum of linear fractional functions. Journal of Inequalities and Applications 63 (2018) https://doi.org/10.1186/s13660-018-1651-9 |