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Title: Large-scale sequential quadratic programming algorithms

The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use ofmore » incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.« less
Authors:
Publication Date:
OSTI Identifier:
10102731
Report Number(s):
SOL--92-4
ON: DE93002528; CNN: Grant DDM-9204208; Grant N00014-90-J-1242
DOE Contract Number:
FG03-92ER25117
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: Sep 1992
Research Org:
Stanford Univ., CA (United States). Systems Optimization Lab.
Sponsoring Org:
USDOE, Washington, DC (United States);Department of Defense, Washington, DC (United States);National Science Foundation, Washington, DC (United States)
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; NONLINEAR PROGRAMMING; ALGORITHMS; FUNCTIONS; NEWTON METHOD; LAGRANGIAN FUNCTION; CONVERGENCE 990200; MATHEMATICS AND COMPUTERS