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20
Sequential Quadratic Programming
, 1995
"... this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can ..."
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Cited by 114 (2 self)
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this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can
A Sqp Method For General Nonlinear Programs Using Only Equality Constrained Subproblems
 MATHEMATICAL PROGRAMMING
, 1993
"... In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [34] it is much simpler to implement and allows any kind of changes of the working s ..."
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Cited by 46 (2 self)
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In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [34] it is much simpler to implement and allows any kind of changes of the working set in every step. Our method relies on a strong regularity condition. As far as it is applicable the new approach is superior to conventional SQPmethods, as demonstrated by extensive numerical tests.
A reduced Hessian method for largescale constrained optimization
 SIAM JOURNAL ON OPTIMIZATION
, 1995
"... ..."
Quadratically And Superlinearly Convergent Algorithms For The Solution Of Inequality Constrained Minimization Problems
, 1995
"... . In this paper some Newton and quasiNewton algorithms for the solution of inequality constrained minimization problems are considered. All the algorithms described produce sequences fx k g converging qsuperlinearly to the solution. Furthermore, under mild assumptions, a qquadratic convergence ra ..."
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Cited by 17 (6 self)
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. In this paper some Newton and quasiNewton algorithms for the solution of inequality constrained minimization problems are considered. All the algorithms described produce sequences fx k g converging qsuperlinearly to the solution. Furthermore, under mild assumptions, a qquadratic convergence rate in x is also attained. Other features of these algorithms are that the solution of linear systems of equations only is required at each iteration and that the strict complementarity assumption is never invoked. First the superlinear or quadratic convergence rate of a Newtonlike algorithm is proved. Then, a simpler version of this algorithm is studied and it is shown that it is superlinearly convergent. Finally, quasiNewton versions of the previous algorithms are considered and, provided the sequence defined by the algorithms converges, a characterization of superlinear convergence extending the result of Boggs, Tolle and Wang is given. Key Words. Inequality constrained optimization, New...
A Parallel Reduced Hessian SQP Method for Shape Optimization
"... We present a parallel reduced Hessian SQP method for smooth shape optimization of systems governed by nonlinear boundary value problems, for the case when the number of shape variables is much smaller than the number of state variables. The method avoids nonlinear resolution of the state equation ..."
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Cited by 13 (4 self)
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We present a parallel reduced Hessian SQP method for smooth shape optimization of systems governed by nonlinear boundary value problems, for the case when the number of shape variables is much smaller than the number of state variables. The method avoids nonlinear resolution of the state equations at each design iteration by embedding them as equality constraints in the optimization problem. It makes use of a decomposition into nonorthogonal subspaces that exploits Jacobian and Hessian sparsity in an optimal fashion. The resulting algorithm requires the solution at each iteration of just two linear systems whose coefficients matrices are the state variable Jacobian of the state equations, i.e. the stiffness matrix, and its transpose. The construction and solution of each of these two systems is performed in parallel, as are sensitivity computations associated with the state variables. The conventional parallelism present in a parallel PDE solverboth constructing and solvi...
Optimal Control Of Two And ThreeDimensional Incompressible NavierStokes Flows
, 1997
"... . The focus of this work is on the development of largescale numerical optimization methods for optimal control of steady incompressible NavierStokes flows. The control is affected by the suction or injection of fluid on portions of the boundary, and the objective function represents the rate at w ..."
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Cited by 10 (3 self)
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. The focus of this work is on the development of largescale numerical optimization methods for optimal control of steady incompressible NavierStokes flows. The control is affected by the suction or injection of fluid on portions of the boundary, and the objective function represents the rate at which energy is dissipated in the fluid. We develop reduced Hessian sequential quadratic programming methods that avoid converging the flow equations at each iteration. Both quasiNewton and Newton variants are developed, and compared to the approach of eliminating the flow equations and variables, which is effectively the generalized reduced gradient method. Optimal control problems are solved for twodimensional flow around a cylinder and threedimensional flow around a sphere. The examples demonstrate at least an orderofmagnitude reduction in time taken, allowing the optimal solution of flow control problems in as little as half an hour on a desktop workstation. Key words. optimal contr...
Optimum Shape Design of Turbine Blades
, 1995
"... this paper the cputime for the computation was 22 minutes on an IBM/RS6000. ..."
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Cited by 8 (6 self)
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this paper the cputime for the computation was 22 minutes on an IBM/RS6000.
Partially Reduced SQP Methods For LargeScale Nonlinear Optimization Problems
, 1997
"... this paper we investigate more closely the structures of two application examples which can be considered representative for the rather wide class of largescale optimization problems in so far as they stem from discretizations: ..."
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Cited by 5 (0 self)
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this paper we investigate more closely the structures of two application examples which can be considered representative for the rather wide class of largescale optimization problems in so far as they stem from discretizations:
On the realization of the Wolfe conditions in reduced quasiNewton methods for equality constrained optimization
 SIAM Journal on Optimization
, 1997
"... Abstract. This paper describes a reduced quasiNewton method for solving equality constrained optimization problems. A major difficulty encountered by this type of algorithm is the design of a consistent technique for maintaining the positive definiteness of the matrices approximating the reduced He ..."
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Cited by 5 (0 self)
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Abstract. This paper describes a reduced quasiNewton method for solving equality constrained optimization problems. A major difficulty encountered by this type of algorithm is the design of a consistent technique for maintaining the positive definiteness of the matrices approximating the reduced Hessian of the Lagrangian. A new approach is proposed in this paper. The idea is to search for the next iterate along a piecewise linear path. The path is designed so that some generalized Wolfe conditions can be satisfied. These conditions allow the algorithm to sustain the positive definiteness of the matrices from iteration to iteration by a mechanism that has turned out to be efficient in unconstrained optimization.
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