Trust region methods for structural optimization using exact second order sensitivity

The performance of multiplier algorithms for structural optimization has been significantly improved by using trust regions. The trust regions are constructed using analytical second order sensitivity, and within this region, the augmented Lagrangian ϕ is minimized subject to bounds. Evaluation of first and second derivatives of ϕ by the adjoint method does not require derivations of individual (implicit) constraint functions, which makes the method economical. Eight test problems are considered and a vast improvement over previously used multiplier algorithms has been noted. Also, the algorithm is robust with respect to scaling, input parameters and starting designs.

[1]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[2]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[3]  S. Goldfeld,et al.  Maximization by Quadratic Hill-Climbing , 1966 .

[4]  G. Vanderplaats,et al.  Structural optimization by methods of feasible directions. , 1973 .

[5]  Edward J. Haug,et al.  Second-order design sensitivity analysis of structural systems , 1981 .

[6]  Jasbir S. Arora,et al.  Potential of transformation methods in optimal design , 1981 .

[7]  Jorge J. Moré,et al.  Recent Developments in Algorithms and Software for Trust Region Methods , 1982, ISMP.

[8]  D. Sorensen.  Newton's method with a model trust region modification , 1982 .

[9]  Ashok Dhondu Belegundu,et al.  A Study of Mathematical Programming Methods for Structural Optimization , 1985 .

[10]  A. Belegundu,et al.  A Computational Study of Transformation Methods for Optimal Design , 1984 .

[11]  J. Arora,et al.  A recursive quadratic programming method with active set strategy for optimal design , 1984 .

[12]  M. J. D. Powell,et al.  On the global convergence of trust region algorithms for unconstrained minimization , 1984, Math. Program..

[13]  A. Vardi.  A Trust Region Algorithm for Equality Constrained Minimization: Convergence Properties and Implementation , 1985 .

[14]  Ashok D. Belegundu,et al.  Lagrangian Approach to Design Sensitivity Analysis , 1985 .

[15]  J. Vial,et al.  A restricted trust region algorithm for unconstrained optimization , 1985 .

[16]  Ya-Xiang Yuan,et al.  Conditions for convergence of trust region algorithms for nonsmooth optimization , 1985, Math. Program..

[17]  Richard H. Byrd,et al.  A Trust Region Algorithm for Nonlinearly Constrained Optimization , 1987 .

[18]  Raphael T. Haftka,et al.  First- and Second-Order Sensitivity Analysis of Linear and Nonlinear Structures , 1986 .

[19]  J. S. Arora,et al.  Dynamic Response Optimization of Mechanical Systems With Multiplier Methods , 1989 .