Update formulas in quasi-Newton methods and parametric programming

[目次]

  • TABLE OF CONTENTS / p1
  • Acknowledgments / p3
  • Notations / p4
  • Chapter1.INTRODUCTION / p1
  • 1.1.Optimization Problems / p1
  • Chapter2.STABILITY OF THE GENERAL GRADIENT METHODS FOR FUNCTION MINIMIZATION / p7
  • 2.1.Introduction / p7
  • 2.2.Minimizer of Nonlinear Function / p8
  • 2.3.Stability of Difference System / p12
  • 2.4.Algorithm and Numerical Experiments / p14
  • Chapter3.UPDATES FORMULAS IN QUASI-NEWTON METHODS FOR FUNCTION MINIMIZATION / p17
  • 3.1.Introduction / p17
  • 3.2.Sparse Updates for Quasi-Newton Methods / p19
  • 3.3.Sparse Symmetric Updates for Quasi-Newton Methods / p21
  • 3.4.Local and Superlinear Convergence / p25
  • Chapter4.FACTORIZATION IN QUASI-NEWTON UPDATE / p29
  • 4.1.Introduction / p29
  • 4.2.Factorized Form in Symmetric Positive Definite Updates / p31
  • 4.3.Triangular Decomposition Form / p33
  • 4.4.Algorithm for Calculating μ=[数式] / p36
  • Chapter5.SOME MODIFICATIONS OF SEQUENTIAL QUADRATIC PROGRAMMING METHOD FOR CONSTRAINED OPTIMIZATION / p39
  • 5.1.Introduction / p39
  • 5.2.Sequential Quadratic Programming Method / p40
  • 5.3.SQP Method with Factorized Quasi-Newton Update / p43
  • 5.4.SQP Method for Constrained Nonlinear Least Squares Problems / p46
  • 5.5.Numerical Examples / p50
  • 5.6.Concluding Remarks / p52
  • Chapter6.NUMERICAL METHOD FOR THE SOLUTION OF A PARAMETRIC CONVEX QUADRATIC PROGRAM / p53
  • 6.1.Introduction / p53
  • 6.2.Some Properties of PQPP(6.1.1) / p54
  • 6.3.Dual Algorithm / p56
  • 6.4.Application of Dual Algorithm / p58
  • 6.5.Numerical Examples / p61
  • References / p67

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この本の情報

書名 Update formulas in quasi-Newton methods and parametric programming
著作者等 高橋 悟
書名別名 準ニュートン法の更新公式とパラメトリック計画法
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