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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...
Analysis of the LagrangeSQPNewton method for the control of a Phase field equation
 Virginia Polytechnic Institute and State Unversity, ICAM Report
, 1999
"... This paper investigates the local convergence of the LagrangeSQPNewtonmethod applied to an optimal control problem governed by a phase field equation with distributed control. The phase field equation is a system of two semilinear parabolic differential equations. Stability analysis of optimizatio ..."
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Cited by 20 (4 self)
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This paper investigates the local convergence of the LagrangeSQPNewtonmethod applied to an optimal control problem governed by a phase field equation with distributed control. The phase field equation is a system of two semilinear parabolic differential equations. Stability analysis of optimization problems and regularity results for parabolic differential equations are used to proof convergence of the controls with respect to the L 2 (Q) norm and with respect to the L 1 (Q) norm.
An SQP Method for the Optimal Control of a Nonlinear Heat Equation
 Control and Cybernetics
, 1994
"... . We investigate local convergence of an SQP method for an optimal control problem governed by the onedimensional heat equation with nonlinear boundary condition. Sufficient conditions for local quadratic convergence of the method based are discussed. AMS subject classification. 49M05, 49M40, 49K2 ..."
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Cited by 16 (4 self)
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. We investigate local convergence of an SQP method for an optimal control problem governed by the onedimensional heat equation with nonlinear boundary condition. Sufficient conditions for local quadratic convergence of the method based are discussed. AMS subject classification. 49M05, 49M40, 49K24. Keywords. LagrangeNewton method, sequential quadratic programming, optimal control, heat equation, nonlinear boundary condition, control constraints. 1 Introduction The LagrangeNewton method is obtained by applying Newton's method or a generalized version of it to find a stationary point of the Lagrangian function associated to a nonlinear optimization problem. If a constraint qualification and a strong second order sufficiency condition are satisfied, the LagrangeNewton method defines a sequential quadratic programming (SQP) algorithm. It is known since several years that the SQP algorithm exhibits local quadratic convergence in finitedimensional spaces. The method can be easily ...
RICE UNIVERSITY The Use of Optimization Techniques in the Solution of Partial Differential Equations from
, 1996
"... Acknowledgments This thesis is a very important milestone in a journey I began more than ten years ago. People too numerous to mention have helped me along the way; a few are singled out here. When I was an undergraduate at the University of Maryland, Baltimore County, the Mathematics faculty, in pa ..."
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Acknowledgments This thesis is a very important milestone in a journey I began more than ten years ago. People too numerous to mention have helped me along the way; a few are singled out here. When I was an undergraduate at the University of Maryland, Baltimore County, the Mathematics faculty, in particular Professors James Greenberg, So/ren Jensen, and Marc Teboulle, taught me to love applied mathematics; their patience with me was endless and I will always be grateful to them.