Practical Aspects Of Variable Reduction Formulations And Reduced Basis Algorithms In Multidisciplina

Abstract : This paper discusses certain connections between nonlinear programming algorithms and the formulation of optimization problems for systems governed by state constraints. The major points of this paper are the detailed calculation of the sensitivities associated with different formulations of optimization problems and the identification of some useful relationships between different formulations. These relationships have practical consequences; if one uses a reduced basis nonlinear programming algorithm, then the implementations for the different formulations need only differ in a single step. (AN)

[1]  John E. Dennis,et al.  A Global Convergence Theory for General Trust-Region-Based Algorithms for Equality Constrained Optimization , 1997, SIAM J. Optim..

[2]  R. A. Tapia,et al.  QUASI-NEWTON METHODS FOR EQUALITY CONSTRAINED OPTIMIZATION: EQUIVALENCE OF EXISTING METHODS AND A NEW IMPLEMENTATION , 1978 .

[3]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[4]  Leon S. Lasdon,et al.  Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming , 1978, TOMS.

[5]  Philip E. Gill,et al.  Practical optimization , 1981 .

[6]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[7]  N. Alexandrov Multilevel algorithms for nonlinear equations and equality constrained optimization , 1993 .

[8]  Tunc Geveci,et al.  Advanced Calculus , 2014, Nature.

[9]  Shirley Dex,et al.  JR 旅客販売総合システム(マルス)における運用及び管理について , 1991 .

[10]  James E. Dennis,et al.  A Comparison of Nonlinear Programming Approaches to an Elliptic Inverse Problem and a New Domain Dec , 1994 .

[11]  John E. Dennis,et al.  Problem Formulation for Multidisciplinary Optimization , 1994, SIAM J. Optim..

[12]  M. El-Alem A global convergence theory for the Celis-Dennis-Tapia trust-region algorithm for constrained optimization , 1991 .

[13]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[14]  Kamy Sepehrnoori,et al.  Optimal Hydrocarbon Reservoir Production Policies , 1986, Oper. Res..