求解凸可行问题的有效算法
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摘要
将束方法与信赖域技巧相结合,提出了求解凸可行问题的有效算法,得出了算法的全局收敛性结果.数值实验结果表明:与已有算法相比,该算法具有较高的运算效率和精度,在求解凸可行问题时是行之有效的.
By combining the bundle method with the trust region technique,an effective algorithm was proposed for solving the convex feasible problem.The global convergence result of the algorithm was also obtained.Compared with some existed algorithms,the present algorithm is valid and has faster convergence speed.
By combining the bundle method with the trust region technique,an effective algorithm was proposed for solving the convex feasible problem.The global convergence result of the algorithm was also obtained.Compared with some existed algorithms,the present algorithm is valid and has faster convergence speed.
引文
[1] BAUSCHKE H H,BORWEIN J M.On projection algorithms for solving convex feasibility problems[J].SIAM Review,1996,38(3):367-426.
[2] GARC′IA-PALOMARESUM,GONZ′ALEZ-CASTANO F J.Incomplete projection algorithms for solving the convex feasibility problem[J].Numerical Algorithms,1998,18(2):177-193.
[3] CHINNECK J W.The constraint consensus method for finding approximately feasible points in nonlinear programs[J].Informs Journal on Computing,2004,16:255-265.
[4]高岩.仿射非线性控制系统生存性的判别[J].控制理论与应用,2009,26(6):654-656.
[5] GAO Y.Viability criteria for differential inclusions[J].Journal of Systems Science and Complexity,2011,24(5):825-834.
[6] GOULD N I.How good are projection methods for convex feasibility problems[J].Computational Optimization and Applications,2008,40(1):1-12.
[7] LI L,GAO Y.Projection algorithm with line search for solving the convex feasibility problem[J].Journal Information Computing Scirence,2008,3(1):62-68.
[8] MARUSTER S,POPIRLAN C.On the Mann-type iteration and the convex feasibility problem[J].Journal of Computational and Applied Mathathematics,2008,212(2):390-396.
[9] DANG Y Z,GAO Y.New algorithms for a convex feasibility problem[J].Chinese Journal of Engineering Mathematics,2013,30(2):283-292.
[10]党亚峥,薛中会.凸可行问题的平行近似次梯度算法[J].运筹学学报,2015,19(1):117-124.
[11]边馥萍.非光滑逐点最大凸函数的束方法[J].天津大学学报,1993(1):110-116.
[2] GARC′IA-PALOMARESUM,GONZ′ALEZ-CASTANO F J.Incomplete projection algorithms for solving the convex feasibility problem[J].Numerical Algorithms,1998,18(2):177-193.
[3] CHINNECK J W.The constraint consensus method for finding approximately feasible points in nonlinear programs[J].Informs Journal on Computing,2004,16:255-265.
[4]高岩.仿射非线性控制系统生存性的判别[J].控制理论与应用,2009,26(6):654-656.
[5] GAO Y.Viability criteria for differential inclusions[J].Journal of Systems Science and Complexity,2011,24(5):825-834.
[6] GOULD N I.How good are projection methods for convex feasibility problems[J].Computational Optimization and Applications,2008,40(1):1-12.
[7] LI L,GAO Y.Projection algorithm with line search for solving the convex feasibility problem[J].Journal Information Computing Scirence,2008,3(1):62-68.
[8] MARUSTER S,POPIRLAN C.On the Mann-type iteration and the convex feasibility problem[J].Journal of Computational and Applied Mathathematics,2008,212(2):390-396.
[9] DANG Y Z,GAO Y.New algorithms for a convex feasibility problem[J].Chinese Journal of Engineering Mathematics,2013,30(2):283-292.
[10]党亚峥,薛中会.凸可行问题的平行近似次梯度算法[J].运筹学学报,2015,19(1):117-124.
[11]边馥萍.非光滑逐点最大凸函数的束方法[J].天津大学学报,1993(1):110-116.