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一类模糊半定规划问题的解法 被引量：1

An Algorithm for a Class of Fuzzy Semi-definite Programming Problem
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摘要 由于内点法的发现和半定规划在控制论、组合优化、统计学等方面的重要应用,半定规划近几年来已成为优化中最活跃的领域。然而许多实际问题很难将它们的目标函数和约束函数精确地描述出来,因此有必要将模糊集理论应用到半定规划中来,进而通过求解模糊半定规划使问题得以解决。 Because of the discovery of interior-point methods and the important application of semi-definite programming in cybernetics, combinatorial optimization, statistics, etc. , semi-definite programming has been the most active one in optimization areas in recent years. Nevertheless, it is hard to accurately describe the objective function and constraints of many practical problems, therefore, it is necessary to introduce fuzzy set theory into semi-definite programming, then proceed to obtain the optimal solution of the problem by solving fuzzy semi-definite programming.
作者 房亮
机构地区 泰山学院数学与系统科学系
出处 《山东科技大学学报（自然科学版）》 CAS 2007年第1期94-95,共2页 Journal of Shandong University of Science and Technology(Natural Science)
关键词 模糊半定规划 模糊集 隶属度函数 fuzzy semi-definite programming, fuzzy set, membership function
分类号 O221.2 [理学—运筹学与控制论]
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参考文献5

  • 1L.Vandenberghe,S.Boyd.Semidefinite programing[J].SIAM Rev.,1996,38:49-95.
  • 2M.J.Todd.Semidefinite optimization[J].Acta Numerica,2001,(10):515-560.
  • 3H.Halicha.Analyticity of the central path at the boundary point in semidefinite programming[R].Technical Report April,Faculty of mathematics,Physics and Informatics,Slovakia:Comenius University,2001.
  • 4R.D.C.Monteiro,T.Tsuchiya.Polynomial convergence of a new family of primal-dual algorithms for semidefinite programming[J].SIAM J.Optimization,1999,(9):551-577.
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同被引文献8

  • 1VANDENBERGHE L, BOYD S. Semidefinite programming[J]. SIAM Review, 1996 (38) :49-95.
  • 2ALIZADEH F. Interior point methods in semidefinite programming with applications to combinatorial optimization[J]. SIAM Journal on Optimization, 1995(5):13-51.
  • 3BENSON H Y,SHANNO D F,VANDERBEI R J. Interior-point methods for nonconvex nonlinear programming: orderings and higher-order methods[J].Mathematical Programming, 2000 (2) : 303-316.
  • 4FLETCHER R, LEYFFER S. Nonlinear programming without a penalty function[J]. Mathematical Programming, 2002 (91) :239-270.
  • 5FLETCHER R,LEYFFER S,TOINT P. A brief history of filter methods[J/OL]. [2006-10-10][2007-12-12]. http:// www. optimization-online.org / DB HTML/ 2006/ 10/ 1489. html.
  • 6FLETCHER R,GOULD N I M, LEYFFER S. Global convergence of trust-region SQP-filter algorithms for general nonlinear programming[J]. SIAM Journal on Optimization,2002(3):635-659.
  • 7UIBRICH M, UIBRICH S,VICENTE L N. A globally convergent primal-dual interior-point filter method for nonlinear programming[J].Mathematical Programming, 2003 (100) : 379-410.
  • 8WACHTER A, BIEGLER L T. Linear search filter methods for nonlinear programming: Local convergence[J]. SIAM Journal on Optimization,2005(16):32-48.

引证文献1

山东科技大学学报（自然科学版）
2007年 第1期

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