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Superlinear and Quadratic Convergence of AffineScaling InteriorPoint Newton Methods for Problems with Simple Bounds without Strict Complementarity Assumption
, 1998
"... A class of affinescaling interiorpoint methods for bound constrained optimization problems is introduced which are locally qsuperlinear or qquadratic convergent. It is assumed that the strong... ..."
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Cited by 21 (3 self)
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A class of affinescaling interiorpoint methods for bound constrained optimization problems is introduced which are locally qsuperlinear or qquadratic convergent. It is assumed that the strong...
A Level Set Approach For The Solution Of A StateConstrained Optimal Control Problem
 Num. Math
, 2004
"... State constrained optimal control problems for linear elliptic partial differential equations are considered. The corresponding first order optimality conditions in primaldual form are analyzed and linked to a free boundary problem resulting in a novel algorithmic approach with the boundary (interf ..."
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Cited by 7 (3 self)
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State constrained optimal control problems for linear elliptic partial differential equations are considered. The corresponding first order optimality conditions in primaldual form are analyzed and linked to a free boundary problem resulting in a novel algorithmic approach with the boundary (interface) between the active and inactive sets as optimization variable. The new algorithm is based on the level set methodology. The speed function involved in the level set equation for propagating the interface is computed by utilizing techniques from shape optimization. Encouraging numerical results attained by the new algorithm are reported on.
Local Convergence of the AffineScaling InteriorPoint Algorithm for Nonlinear Programming
 COMPUT. OPTIM. AND APPL
, 1999
"... This paper addresses the local convergence properties of the anescaling interiorpoint algorithm for nonlinear programming. The analysis of local convergence is developed in terms of parameters that control the interiorpoint scheme and the size of the residual of the linear system that provides the ..."
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Cited by 5 (2 self)
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This paper addresses the local convergence properties of the anescaling interiorpoint algorithm for nonlinear programming. The analysis of local convergence is developed in terms of parameters that control the interiorpoint scheme and the size of the residual of the linear system that provides the step direction. The analysis follows the classical theory for quasiNewton methods and addresses qlinear, qsuperlinear, and qquadratic rates of convergence.
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"... Design of penalty functions for optimal control of linear dynamical systems under state and input constraints ..."
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Design of penalty functions for optimal control of linear dynamical systems under state and input constraints
2012 American Control Conference
, 2012
"... A constructive interior penalty method for optimal control problems with state and input constraints. ..."
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A constructive interior penalty method for optimal control problems with state and input constraints.
An Analysis of Newton's Method for Equivalent KarushKuhnTucker Systems
, 1999
"... In this paper we analyze the application of Newton's method to the solution of systems of nonlinear equations arising from equivalent forms of the firstorder KarushKuhnTucker necessary conditions for constrained optimization. The analysis is carried out by using an abstract model for the ..."
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In this paper we analyze the application of Newton's method to the solution of systems of nonlinear equations arising from equivalent forms of the firstorder KarushKuhnTucker necessary conditions for constrained optimization. The analysis is carried out by using an abstract model for the original system of nonlinear equations and for an equivalent form of this system obtained by a reformulation that appears often when dealing with firstorder KarushKuhn Tucker necessary conditions. The model is used to determine the quantities that bound the difference between the Newton steps corresponding to the two equivalent systems of equations. The model is sufficiently abstract to include the cases of equalityconstrained optimization, minimization with simple bounds, and also a class of discretized optimal control problems. Keywords. Nonlinear programming, Newton's method, firstorder KarushKuhnTucker necessary conditions. AMS subject classifications. 49M37, 90C06, 90C30 1 In...
An Affine Scaling Trust Region Algorithm For Nonlinear Programming
, 2000
"... . A monotonic decrease minimization algorithm can be desirable for nonconvex minimization since there may be more than one local minimizers. A typical interior point algorithm for a convex programming problem does not yield monotonic improvement of the objective function value. In this paper, a mono ..."
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. A monotonic decrease minimization algorithm can be desirable for nonconvex minimization since there may be more than one local minimizers. A typical interior point algorithm for a convex programming problem does not yield monotonic improvement of the objective function value. In this paper, a monotonic a#ne scaling trust region algorithm is proposed for nonconvex programming. The proposed a#ne scaling trust region algorithm is described in the context of minimizing the exact l 1 penalty function. A#ne scaling Newton steps are derived directly from the complementarity conditions. A primal trust region subproblem is proposed for globalization. A dual subproblem is formulated to facilitate dual variables updates; its solution yields decrease of the l 1 function. Global convergence of the proposed algorithm is established. 1. Introduction. Considerable recent research studies have been made in an e#ort to generalize the successful interior point methods for convex programming to nonconve...