平成１３年度第３回KSMAP

日時：１０月４日（木）　１４：００ 〜 １７：００

京都大学 工学部8号館 共同6号室

       会場への案内  

講演題目と講演者

  信頼領域法と最適化問題へのある適用 
   相良信子   （愛知大学経営学部）

  Recent Advances in Concave Programming: theory and algorithms.
   R. Enkhbat  (Mongolian State University)

 1.    信頼領域法(Trust  Region  method)の概要
　               　　　ニュートン法との関係
 2.　 部分問題の解法について
     (a)    Using Exact   Solution   to   Subproblem  
            問題点： Hard  Case
     (b)　 Using   Approximate   Solution   to   Subproblem 
           *   The  Dogleg   Method  
                   ( Cauchy   Point )  
           *    Steihang's   Approach   
                   ( Conjugate  Gradient  Method ) 
           *   Two-Dimensional   Subspace  Minimization
 3.    Global   Convergence
 4.　 信頼領域法を制約つき最適化問題へ適用するときの課題
 5.    制約つき最適化問題への信頼領域法のある適用例

参考文献：  
1.  J.Dennis  and   R.B.Schnabel: Numerical  Methods  for   Unconstrained  
Optimization   and   Nonlinear   Equations,   Prentice-Hall  (1983).   
2.  J.Noceldal  and  S.J.Wright: Numerical  Optimization,   Springer (1999).
3.  R.Fletcher: Practical  Methods of   Optimization (Second  Edition),  
    Wiley(1987).   

   The talk is devoted to recent 
  development and applications of concave programming or
  concave minimization problems. First we servey  existing 
  algorithms and methods, and then consider new global
  optimality  conditions for minimizing a concave function 
  over an arbitrary set. We will mainly focus on methods and
  algorithms based on the global optimality conditions.
  Some numerical results as well as applications
  of concave programming are provided. Also further
  generalization of concave programming to the
  quasiconvex case is reported.