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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.
Analysis of Inexact TrustRegion SQP Algorithms
 RICE UNIVERSITY, DEPARTMENT OF
, 2000
"... In this paper we extend the design of a class of compositestep trustregion SQP methods and their global convergence analysis to allow inexact problem information. The inexact problem information can result from iterative linear systems solves within the trustregion SQP method or from approximatio ..."
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Cited by 26 (2 self)
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In this paper we extend the design of a class of compositestep trustregion SQP methods and their global convergence analysis to allow inexact problem information. The inexact problem information can result from iterative linear systems solves within the trustregion SQP method or from approximations of firstorder derivatives. Accuracy requirements in our trustregion SQP methods are adjusted based on feasibility and optimality of the iterates. Our accuracy requirements are stated in general terms, but we show how they can be enforced using information that is already available in matrixfree implementations of SQP methods. In the absence of inexactness our global convergence theory is equal to that of Dennis, ElAlem, Maciel (SIAM J. Optim., 7 (1997), pp. 177207). If all iterates are feasible, i.e., if all iterates satisfy the equality constraints, then our results are related to the known convergence analyses for trustregion methods with inexact gradient information fo...
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...
A TRUNCATED SQP METHOD BASED ON INEXACT INTERIORPOINT SOLUTIONS OF SUBPROBLEMS ∗
"... Abstract. We consider sequential quadratic programming (SQP) methods applied to optimization problems with nonlinear equality constraints and simple bounds. In particular, we propose and analyze a truncated SQP algorithm in which subproblems are solved approximately by an infeasible predictorcorrec ..."
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Cited by 6 (5 self)
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Abstract. We consider sequential quadratic programming (SQP) methods applied to optimization problems with nonlinear equality constraints and simple bounds. In particular, we propose and analyze a truncated SQP algorithm in which subproblems are solved approximately by an infeasible predictorcorrector interiorpoint method, followed by setting to zero some variables and some multipliers so that complementarity conditions for approximate solutions are enforced. Verifiable truncation conditions based on the residual of optimality conditions of subproblems are developed to ensure both global and fast local convergence. Global convergence is established under assumptions that are standard for linesearch SQP with exact solution of subproblems. The local superlinear convergence rate is shown under the weakest assumptions that guarantee this property for pure SQP with exact solution of subproblems, namely, the strict Mangasarian–Fromovitz constraint qualification and secondorder sufficiency. Local convergence results for our truncated method are presented as a special case of the local convergence for a more general perturbed SQP framework, which is of independent interest and is applicable even to some algorithms whose subproblems are not quadratic programs. For example, the framework can also be used to derive sharp local convergence results for linearly constrained Lagrangian methods. Preliminary numerical results confirm that it can be indeed beneficial to solve subproblems approximately, especially on early iterations. Key words. sequential quadratic programming, inexact sequential quadratic programming, truncated sequential quadratic programming, interiorpoint method, superlinear convergence