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

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 SQP-methods, as demonstrated by extensive numerical tests.

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. In this paper some Newton and quasi-Newton algorithms for the solution of inequality constrained minimization problems are considered. All the algorithms described produce sequences fx k g converging q-superlinearly to the solution. Furthermore, under mild assumptions, a q-quadratic 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 Newton-like algorithm is proved. Then, a simpler version of this algorithm is studied and it is shown that it is superlinearly convergent. Finally, quasi-Newton 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...

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 solver---both constructing and solvi...

. The focus of this work is on the development of large-scale numerical optimization methods for optimal control of steady incompressible Navier-Stokes 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 quasi-Newton 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 two-dimensional flow around a cylinder and three-dimensional flow around a sphere. The examples demonstrate at least an order-of-magnitude 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...

this paper the cpu-time for the computation was 22 minutes on an IBM/RS6000.

this paper we investigate more closely the structures of two application examples which can be considered representative for the rather wide class of large-scale optimization problems in so far as they stem from discretizations:

this paper we present an algorithm for turbomachinery optimal blade-to-blade (S1-streamsurface) 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/boundary-layer solver that is widely used in engineering practice. 1 Introduction

this paper is to determine the cross-sectional shape of a blade in a turbomachine in order to reproduce as well as possible a given velocity profile of the flow around the blade. It is formulated as a least squares minimization problem and solved in a simultaneous optimization approach. The focus of the paper lies on two aspects: (1) the partially reduced SQP method applied to solve the resulting constrained optimization problem and (2) the construction of the multigrid algorithm for the solution of the large scale adjoint systems. 1. Introduction