Results 1  10
of
46
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 ..."
Abstract

Cited by 164 (4 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 69 (2 self)
 Add to MetaCart
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.
An interior point algorithm for largescale nonlinear . . .
, 2002
"... Nonlinear programming (NLP) has become an essential tool in process engineering, leading to prot gains through improved plant designs and better control strategies. The rapid advance in computer technology enables engineers to consider increasingly complex systems, where existing optimization codes ..."
Abstract

Cited by 62 (3 self)
 Add to MetaCart
Nonlinear programming (NLP) has become an essential tool in process engineering, leading to prot gains through improved plant designs and better control strategies. The rapid advance in computer technology enables engineers to consider increasingly complex systems, where existing optimization codes reach their practical limits. The objective of this dissertation is the design, analysis, implementation, and evaluation of a new NLP algorithm that is able to overcome the current bottlenecks, particularly in the area of process engineering. The proposed algorithm follows an interior point approach, thereby avoiding the combinatorial complexity of identifying the active constraints. Emphasis is laid on exibility in the computation of search directions, which allows the tailoring of the method to individual applications and is mandatory for the solution of very large problems. In a fullspace version the method can be used as general purpose NLP solver, for example in modeling environments such as Ampl. The reduced space version, based on coordinate decomposition, makes it possible to tailor linear algebra
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 ..."
Abstract

Cited by 56 (18 self)
 Add to MetaCart
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.
A reduced Hessian method for largescale constrained optimization
 SIAM JOURNAL ON OPTIMIZATION
, 1995
"... ..."
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 ..."
Abstract

Cited by 46 (9 self)
 Add to MetaCart
(Show Context)
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...
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 ..."
Abstract

Cited by 38 (12 self)
 Add to MetaCart
. 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...
Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters
, 1997
"... A model algorithm based on the successive quadratic programming method for solving the general nonlinear programming problem is presented. The objective function and the constraints of the problem are only required to be differentiable and their gradients to satisfy a Lipschitz condition. The strate ..."
Abstract

Cited by 23 (9 self)
 Add to MetaCart
A model algorithm based on the successive quadratic programming method for solving the general nonlinear programming problem is presented. The objective function and the constraints of the problem are only required to be differentiable and their gradients to satisfy a Lipschitz condition. The strategy for obtaining global convergence is based on the trust region approach. The merit function is a type of augmented Lagrangian. A new updating scheme is introduced for the penalty parameter, by means of which monotone increase is not necessary. Global convergence results are proved and numerical experiments are presented.
Global and local convergence of line search filter methods for nonlinear programming
, 1521
"... Line search methods for nonlinear programming using Fletcher and Leyffer’s filter method, which replaces the traditional merit function, are proposed and their global and local convergence properties are analyzed. Previous theoretical work on filter methods has considered trust region algorithms and ..."
Abstract

Cited by 18 (4 self)
 Add to MetaCart
(Show Context)
Line search methods for nonlinear programming using Fletcher and Leyffer’s filter method, which replaces the traditional merit function, are proposed and their global and local convergence properties are analyzed. Previous theoretical work on filter methods has considered trust region algorithms and only the question of global convergence. The presented framework is applied to barrier interior point and active set SQP algorithms. Under mild assumptions it is shown that every limit point of the sequence of iterates generated by the algorithm is feasible, and that there exists at least one limit point that is a stationary point for the problem under consideration. Furthermore, it is shown that the proposed methods do not suffer from the Maratos effect if the search directions are improved by second order corrections, so that fast local convergence to strict local solutions is achieved. A new alternative filter approach employing the Lagrangian function instead of the objective function with identical global convergence properties is briefly discussed.
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 ..."
Abstract

Cited by 15 (4 self)
 Add to MetaCart
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...