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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 ..."
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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...
On the Convergence Theory of TrustRegionBased Algorithms for EqualityConstrained Optimization
, 1995
"... In this paper we analyze incxact trust region interior point (TRIP) sequential quadr tic programming (SOP) 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 ..."
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Cited by 8 (0 self)
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In this paper we analyze incxact trust region interior point (TRIP) sequential quadr tic programming (SOP) 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 nonhnear constraints often come from the discretization of partial differential equations. In such cases the calculation of derivative information and the solution of hncarizcd equations is expensive. Often, the solution of hncar systems and derivatives arc computed incxactly yielding nonzero residuals. This paper
Domain Decomposition Methods for LinearQuadratic Elliptic Optimal Control Problems
, 2004
"... This thesis is concerned with the development of domain decomposition (DD) based preconditioners for linearquadratic elliptic optimal control problems (LQEOCPs), their analysis, and numerical studies of their performance on model problems. The solution of LQEOCPs arises in many applications, ei ..."
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Cited by 2 (1 self)
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This thesis is concerned with the development of domain decomposition (DD) based preconditioners for linearquadratic elliptic optimal control problems (LQEOCPs), their analysis, and numerical studies of their performance on model problems. The solution of LQEOCPs arises in many applications, either directly or as subproblems in Newton or Sequential Quadratic Programming methods for the solution of nonlinear elliptic optimal control problems. After a finite element discretization, convex LQEOCPs lead to large scale symmetric indefinite linear systems. The solution of these large systems is a very time consuming step and must be done iteratively, typically with a preconditioned Krylov subspace method. Developing good preconditioners for these linear systems is an important part of improving the overall performance of the solution method. The DD