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Analysis of Inexact TrustRegion InteriorPoint SQP Algorithms
, 1995
"... In this paper we analyze inexact trustregion interiorpoint (TRIP) sequential quadratic programming (SQP) algorithms for the solution of optimization problems with nonlinear equality constraints and simple bound constraints on some of the variables. Such problems arise in many engineering applicati ..."
Abstract

Cited by 11 (7 self)
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In this paper we analyze inexact trustregion interiorpoint (TRIP) sequential quadratic programming (SQP) algorithms for the solution of optimization problems with nonlinear equality constraints and simple bound constraints on some of the variables. Such problems arise in many engineering applications, in particular in optimal control problems with bounds on the control. The nonlinear constraints often come from the discretization of partial differential equations. In such cases the calculation of derivative information and the solution of linearized equations is expensive. Often, the solution of linear systems and derivatives are computed inexactly yielding nonzero residuals. This paper analyzes the effect of the inexactness onto the convergence of TRIP SQP and gives practical rules to control the size of the residuals of these inexact calculations. It is shown that if the size of the residuals is of the order of both the size of the constraints and the trustregion radius, t...
A MemoryConserving Hybrid Method For Solving Linear Systems With Multiple Right Hand Sides
 Center for Supercomputing Research and Development, University of Illinois at UrbanaChampaign
, 1992
"... . We propose a method for the solution of sparse linear, nonsymmetric systems AX = B where A is a sparse and nonsymmetric matrix of order n while B is an arbitrary rectangular matrix of order n \Theta s with s of moderate size. The method uses a single Krylov subspace per step as a generator of app ..."
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Cited by 4 (1 self)
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. We propose a method for the solution of sparse linear, nonsymmetric systems AX = B where A is a sparse and nonsymmetric matrix of order n while B is an arbitrary rectangular matrix of order n \Theta s with s of moderate size. The method uses a single Krylov subspace per step as a generator of approximations, a projection process, and a Richardson acceleration technique. It thus combines the advantages of recent hybrid methods with those for solving symmetric systems with multiple right hand sides. Numerical experiments indicate that provided hybrid techniques are applicable, the method has significantly lower memory requirements and better practical performance than block versions of nonsymmetric solvers such as GMRES. Unlike block BCG it does not require the use of the transpose, it is not sensitive to the right hand sides and it can be used even when not all the elements of B are simultaneously available. AMS(MOS) subject classifications. 65F10,65Y20 1. Introduction. We consider ...