Global Optimization Approach to Non-convex Problems
Global Optimization Approach to Non-convex Problems
摘要
A new approach to find the global optimal solution of the special non-convex problems is proposed in this paper. The non-convex objective problem is first decomposed into two convex sub-problems. Then a generalized gradient is introduced to determine a search direction and the evolution equation is built to obtain a global minimum point. By the approach, we can prevent the search process from some local minima and search a global minimum point. Two numerical examples are given to prove the approach to be effective.
参考文献17
-
1[1]BILBRO G L. Fast stochastic global optimization[J]. IEEE Trans System Man Cybernetics, 1995, 24(4): 684-689.
-
2[2]KIRKPATRICK S, GELATT C D. Jr, VECCHI M P. Optimization by simulated annealing [J]. Science, 1983, 220: 671-680.
-
3[3]RENDERS J M, FLASSE S P. Hybrid method using genetic algorithms for global optimization[J]. IEEE Trans on System Man Cybernetics: Part B, 1996, 26(2):243-258.
-
4[4]LI B, JIANG W S. A novel stochastic optimization algorithm[J]. IEEE Trans on System Man Cybernetics: Part B, 2000, 30(1): 193-198.
-
5[5]CHOWDHURY P R, SINGH Y P, CHANSARKAR R A. Hybridization of gradient descent algorithms with tunneling methods for global optimization[J]. IEEE Trans on System Man Cybernetics: Part A, 2000, 30(3): 384-390.
-
6[6]ZOU Mou-yan, ZOU Xi. Global optimization: An auxiliary cost function approach [J]. IEEE Trans on System Man Cybernetics: Part A, 2000, 30(3):347-354.
-
7[7]BARHEN J, PROTOPOPESCU V, REISTER D. Trust: A deterministic algorithm for global optimization[J]. Science, 1997, 276:1094-1097.
-
8[8]KAUL R N, SUNEJA S K, LALITHA C S. Generalized non-smooth invexity[J]. J Information Optimization Science, 1994, 15:1-17.
-
9[9]DEMYANOV V F, SUTTI C. Representation of the Clarke's sub-differential for a regular quasi-differentiable function[J]. J Optimization Theory and Application, 1995, 87:553-567.
-
10[10]KUNTZ L, PIELCZYK A. The method of common descent for certain class of quasi-differentiable functions[J]. Optimization, 1991, 22:669-679.
-
1SHANGYou-lin LIXiao-yan.A Filled Function with Adjustable Parameters for Unconstrained Global Optimization[J].Chinese Quarterly Journal of Mathematics,2004,19(3):232-239. 被引量：1
-
2ZHAOXinchao.A GREEDY GENETIC ALGORITHM FOR UNCONSTRAINED GLOBAL OPTIMIZATION[J].Journal of Systems Science & Complexity,2005,18(1):102-110. 被引量：6
-
3张贵军,吴惕华,叶蓉,杨海清.Global optimization over linear constraint non-convex programming problem[J].Journal of Harbin Institute of Technology(New Series),2005,12(6):650-655.
-
4丁协平,2何诣然.BEST APPROXIMATION THEOREM FOR SET-VALUED MAPPINGSWITHOUT CONVEX VELUES AND CONTINUITY[J].Applied Mathematics and Mechanics(English Edition),1998,19(9):831-836.
-
5杨志坚.INITIAL-BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM FOR A QUASILINEAR EVOLUTION EQUATION[J].Acta Mathematica Scientia,1999,19(S1):487-496. 被引量：1
-
6张利勋,刘永智,王康宁.Construction of Solution for the Third Order Dispersion Evolution Equation[J].Journal of Electronic Science and Technology of China,2004,2(2):83-86.
-
7BAI Fengtu (North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450045, China) GU Yonggeng (Institute of Systems Science, Academia Sinica, Beijing 100080, China) MIAO Changxing (Institute of Applied Physics and Computational Math.FRACTIONAL ORDER EVOLUTION EQUATIONINTERPOLATING BOTH HEAT AND WAVE EQUATION[J].Systems Science and Mathematical Sciences,1997,10(2):160-167.
-
8刘响林,陈庆辉,张保才.THE SYMMETRY CONSTRAINT AND LEVY EVOLUTION EQUATION HIERARCHY[J].Annals of Differential Equations,1998,14(3):526-533.
-
9LIU Hongxia (Department of Mathematics, Jinan University, Guangzhou 510632, China) PAN Tao (Department of Mathematics and Information Science, Guangxi University, Nanning 530004, China).ASYMPTOTIC STABILITY OF VISCOUS SHOCK PROFILE FOR NON-CONVEX SYSTEM OF ONE-DIMENSIONAL VISCOELASTIC MATERIALS WITH BOUNDARY EFFECT[J].Journal of Systems Science & Complexity,2001,14(4):425-437.
-
10PU Dingguo(Institute of Applied Mathematics, Shanghai Tiedao University, Shanghai 200333, China).THE CONVERGENCE OF BROYDEN ALGORITHMSWITHOUT CONVEXITY ASSUMPTION[J].Systems Science and Mathematical Sciences,1997,10(4):289-298.
