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On the solution of equality constrained quadratic programming problems arising in optimization. (English) Zbl 0999.65050

Summary: We consider the application of the conjugate gradient method to the solution of large equality constrained quadratic programs arising in nonlinear optimization. Our approach is based implicitly on a reduced linear system and generates iterates in the null space of the constraints. Instead of computing a basis for this null space, we choose to work directly with the matrix of constraint gradients, computing projections into the null space by either a normal equations or an augmented system approach.
Unfortunately, in practice such projections can result in significant rounding errors. We propose iterative refinement techniques, as well as an adaptive reformulation of the quadratic problem, that can greatly reduce these errors without incurring high computational overheads. Numerical results illustrating the efficacy of the proposed approaches are presented.

MSC:

65K05 Numerical mathematical programming methods
90C55 Methods of successive quadratic programming type
65F35 Numerical computation of matrix norms, conditioning, scaling
90C06 Large-scale problems in mathematical programming
90C30 Nonlinear programming

Software:

CUTEr; TRICE; mctoolbox
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