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Primaldual Strategy for Constrained Optimal Control Problems
, 1997
"... . An algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed. It is based on an active set strategy involving primal as well as dual variables. For discretized problems sufficient conditions for convergence in finitely many iterations are given. Nume ..."
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Cited by 53 (6 self)
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. An algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed. It is based on an active set strategy involving primal as well as dual variables. For discretized problems sufficient conditions for convergence in finitely many iterations are given. Numerical examples are given and the role of strict complementarity condition is discussed. Keywords: Active Set, Augmented Lagrangian, Primaldual method, Optimal Control. AMS subject classification. 49J20, 49M29 1. Introduction and formulation of the problem. In the recent past significant advances have been made in solving efficiently nonlinear optimal control problems. Most of the proposed methods are based on variations of the sequential quadratic programming (SQP) technique, see for instance [HT, KeS, KuS, K, T] and the references given there. The SQPalgorithm is sequential and each of its iterations requires the solution of a quadratic minimization problem subject to linearized constr...
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 37 (8 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 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...
Computational Strategies For Shape Optimization Of TimeDependent NavierStokes Flows
, 1997
"... . We consider the problem of shape optimization of twodimensional #ows governed by the timedependentNavierStokes equations. For this problem we propose computational strategies with respect to optimization method, sensitivity method, and unstructured meshing scheme. We argue that, despite their s ..."
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Cited by 6 (0 self)
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. We consider the problem of shape optimization of twodimensional #ows governed by the timedependentNavierStokes equations. For this problem we propose computational strategies with respect to optimization method, sensitivity method, and unstructured meshing scheme. We argue that, despite their superiority for steady NavierStokes #ow optimization, reduced sequential quadratic programming #RSQP# methods are too memoryintensive for the timedependent problem. Instead, we advocate a combination of generalized reduced gradients #for the #ow equation constraints# and SQP #for the remaining inequality constraints#. With respect to sensitivity method, wefavor discrete sensitivities, which can be implemented with little additional storage or work beyond that required for solution of the #ow equations, and thus possess a distinct advantage over discretized continuous sensitivities, which require knowledge of the entire time history of the #ow variables. Finally,we takeatwophase approach t...
Parallel NewtonKrylov Methods For PDEConstrained Optimization
 In Proceedings of Supercomputing ’99
, 1999
"... . Large scale optimization of systems governed by partial differential equations (PDEs) is a frontier problem in scientific computation. The stateoftheart for solving such problems is reducedspace quasiNewton sequential quadratic programming (SQP) methods. These take full advantage of existing ..."
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Cited by 4 (0 self)
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. Large scale optimization of systems governed by partial differential equations (PDEs) is a frontier problem in scientific computation. The stateoftheart for solving such problems is reducedspace quasiNewton sequential quadratic programming (SQP) methods. These take full advantage of existing PDE solver technology and parallelize well. However, their algorithmic scalability is questionable; for certain problem classes they can be very slow to converge. In this paper we propose a fullspace NewtonKrylov SQP method that uses the reducedspace quasiNewton method as a preconditioner. The new method is fully parallelizable; exploits the structure of and available parallel algorithms for the PDE forward problem; and is quadratically convergent close to a local minimum. We restrict our attention to boundary value problems and we solve a model optimal flow control problem, with both Stokes and NavierStokes equations as constraints. Algorithmic comparisons, scalability results, and para...
Partially Reduced SQP Methods for Optimal Turbine and Compressor Blade Design
 In Bock et al. (Ed.), Proceedings of the 2nd European Conference on Numerical Mathematics and Advanced Applications
, 1998
"... this paper we present an algorithm for turbomachinery optimal bladetoblade (S1streamsurface) design over a full working range. We formulate the design task as a constrained boundary control multiple setpoint optimization problem in partial di#erential equations and develop a partially reduced SQP ..."
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Cited by 4 (2 self)
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this paper we present an algorithm for turbomachinery optimal bladetoblade (S1streamsurface) design over a full working range. We formulate the design task as a constrained boundary control multiple setpoint optimization problem in partial di#erential equations and develop a partially reduced SQP (PRSQP) algorithm that makes way for an e#cient parallel implementation. We present numerical results based on a 2D coupled Euler/boundarylayer solver that is widely used in engineering practice. 1 Introduction
NUMERICAL SENSITIVITY ANALYSIS FOR THE QUANTITY OF INTEREST IN PDECONSTRAINED OPTIMIZATION
"... Abstract. PDEconstrained optimization problems involving inequality constraints for the design variables are considered. The optimization problems and hence their solutions are subject to perturbations in the data. An output functional (quantity of interest) is given which depends on both the optim ..."
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Cited by 2 (2 self)
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Abstract. PDEconstrained optimization problems involving inequality constraints for the design variables are considered. The optimization problems and hence their solutions are subject to perturbations in the data. An output functional (quantity of interest) is given which depends on both the optimal state and design variables. Conditions are derived such that the quantity of interest at the optimal solution is once and twice differentiable with respect to the perturbation parameters. A procedure is devised for the efficient evaluation of these derivatives. Numerical examples are given. Key words. Sensitivity analysis, PDEconstrained optimization, quantity of interest AMS subject classifications. 1. Introduction. In this paper we consider PDEconstrained optimization problems with inequality constraints. The optimization problems are formulated in a general setting including optimal control as well as parameter identification problems. The problems are subject to perturbation in the data. We suppose to be given a quantity of interest (output functional), which depends on both the state and the
an der Fakultät für Mathematik
, 1864
"... identification problems for elastic large deformations Part I: model and solution of the inverse problem ..."
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identification problems for elastic large deformations Part I: model and solution of the inverse problem
Copyright c○1997, Ajit R. ShenoyOptimization Techniques Exploiting Problem Structure: Applications to Aerodynamic Design
, 1997
"... The research presented in this dissertation investigates the use of allatonce methods applied to aerodynamic design. Allatonce schemes are usually based on the assumption of sufficient continuity in the constraints and objectives, and this assumption can be troublesome in the presence of shock d ..."
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The research presented in this dissertation investigates the use of allatonce methods applied to aerodynamic design. Allatonce schemes are usually based on the assumption of sufficient continuity in the constraints and objectives, and this assumption can be troublesome in the presence of shock discontinuities. Special treatment has to be considered for such problems and we study several approaches. Our allatonce methods are based on the Sequential Quadratic Programming method, and are designed to exploit the structure inherent in a given problem. The first method is a Reduced Hessian formulation which projects the optimization problem to a lower dimension design space. The second method exploits the sparse structure in a given problem which can yield significant savings in terms of computational effort as well as storage requirements. An underlying theme in all our applications is that careful analysis of the given problem can often lead to an efficient implementation of these allatonce methods. Chapter 2 describes a nozzle design problem involving onedimensional transonic flow. An initial formulation as an optimal control problem allows us to solve the problem as as twopoint boundary problem which provides useful insight into the nature of the problem. Using
GLOBALIZATION OF SQPMETHODS IN CONTROL OF THE INSTATIONARY NAVIERSTOKES EQUATIONS
"... Abstract. A numerically inexpensive globalization strategy of sequential quadratic programming methods (SQPmethods) for control of the instationary Navier Stokes equations is investigated. Based on the proper functional analytic setting a convergence analysis for the globalized method is given. It ..."
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Abstract. A numerically inexpensive globalization strategy of sequential quadratic programming methods (SQPmethods) for control of the instationary Navier Stokes equations is investigated. Based on the proper functional analytic setting a convergence analysis for the globalized method is given. It is argued that the a priori formidable SQPstep can be decomposed into linear primal and linear adjoint systems, which is amenable for existing CFLsoftware. A report on a numerical test demonstrates the feasibility of the approach.