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TrustRegion InteriorPoint Algorithms For Minimization Problems With Simple Bounds
 SIAM J. CONTROL AND OPTIMIZATION
, 1995
"... Two trustregion interiorpoint algorithms for the solution of minimization problems with simple bounds are analyzed and tested. The algorithms scale the local model in a way similar to Coleman and Li [1]. The first algorithm is more usual in that the trust region and the local quadratic model are c ..."
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Cited by 56 (18 self)
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Two trustregion interiorpoint algorithms for the solution of minimization problems with simple bounds are analyzed and tested. The algorithms scale the local model in a way similar to Coleman and Li [1]. The first algorithm is more usual in that the trust region and the local quadratic model are consistently scaled. The second algorithm proposed here uses an unscaled trust region. A global convergence result for these algorithms is given and dogleg and conjugategradient algorithms to compute trial steps are introduced. Some numerical examples that show the advantages of the second algorithm are presented.
TrustRegion InteriorPoint SQP Algorithms For A Class Of Nonlinear Programming Problems
 SIAM J. CONTROL OPTIM
, 1997
"... In this paper a family of trustregion interiorpoint SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal co ..."
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Cited by 46 (9 self)
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In this paper a family of trustregion interiorpoint SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal control problems. The algorithms treat states and controls as independent variables. They are designed to take advantage of the structure of the problem. In particular they do not rely on matrix factorizations of the linearized constraints, but use solutions of the linearized state equation and the adjoint equation. They are well suited for large scale problems arising from optimal control problems governed by partial differential equations. The algorithms keep strict feasibility with respect to the bound constraints by using an affine scaling method proposed for a different class of problems by Coleman and Li and they exploit trustregion techniques for equalityconstrained optimizatio...
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 12 (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
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...