Sequential quadratic programming algorithms for optimization
The problem considered is that of finding local minimizers for a function subject to general nonlinear inequality constraints, when first and perhaps second derivatives are available. The methods studied belong to the class of sequential quadratic programming (SQP) algorithms. In particular, the methods are based on the SQP algorithm embodied in the code NPSOL, which was developed at the Systems Optimization Laboratory, Stanford University. The goal of this paper is to develop SQP algorithms that allow some flexibility in their design. Specifically, we are interested in introducing modifications that enable the algorithms to solve large-scale problems efficiently. The following issues are considered in detail: instead of trying to obtain the search direction as a minimizer for the QP, the solution process is terminated after a limited number of iterations. Suitable termination criteria are defined that ensure convergence for an algorithm that uses a quasi-Newton approximation for the full Hessian. For many problems the reduced Hessian is considerably smaller than the full Hessian. Consequently, there are considerable practical benefits to be gained by only requiring an approximation to the reduced Hessian. Theorems are proved concerning the convergence and rate of convergence for an algorithm that uses a quasi-Newton approximation for the reduced Hessian when early termination of the QP subproblem is enforced. The use of second derivatives, while having significant practical advantages, introduces new difficulties; for example, the QP subproblems may be non-convex, and even a minimizer for the subproblem is no longer guaranteed to yield a suitable search direction. Also, theorems are proved for the convergence and rate of convergence of these algorithms. Finally, some numerical results, obtained from a modification of the code NPSOL, are presented. 43 refs., 4 tabs.
- Research Organization:
- Stanford Univ., CA (USA). Systems Optimization Lab.
- Sponsoring Organization:
- USDOD; DOE/ER; National Science Foundation (NSF); SPAIN
- DOE Contract Number:
- FG03-87ER25030
- OSTI ID:
- 5325989
- Report Number(s):
- SOL-89-7; ON: DE90000022; CNN: N00014-87-K-0142; ECS-8715153
- Country of Publication:
- United States
- Language:
- English
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