Results 1 
6 of
6
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 114 (2 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 Global Convergence Theory for General TrustRegionBased Algorithms for Equality Constrained Optimization
 SIAM Journal on Optimization
, 1992
"... This work presents a global convergence theory for a broad class of trustregion algorithms for the smooth nonlinear progro.mmln S problem with equality constraints. The main result generalizes Powell's 1975 result for unconstrained trustregion algorithms. ..."
Abstract

Cited by 42 (10 self)
 Add to MetaCart
This work presents a global convergence theory for a broad class of trustregion algorithms for the smooth nonlinear progro.mmln S problem with equality constraints. The main result generalizes Powell's 1975 result for unconstrained trustregion algorithms.
Reduced SQP Methods for LargeScale Optimal Control Problems in DAE with Application to Path Planning Problems for Satellite Mounted Robots
, 1996
"... and loving encouragement. Contents 1 Introduction 3 1.1 The mathematical problem formulation : : : : : : : : : : : : : : : : : : : : 7 1.2 Notational conventions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2 The Collocation Discretization 11 2.1 Collocation for two point BVP in ..."
Abstract

Cited by 16 (7 self)
 Add to MetaCart
and loving encouragement. Contents 1 Introduction 3 1.1 The mathematical problem formulation : : : : : : : : : : : : : : : : : : : : 7 1.2 Notational conventions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2 The Collocation Discretization 11 2.1 Collocation for two point BVP in ODE : : : : : : : : : : : : : : : : : : : : 11 2.1.1 Choice of collocation points : : : : : : : : : : : : : : : : : : : : : : 14 2.1.2 The polynomial representation : : : : : : : : : : : : : : : : : : : : : 14 2.1.3 A tempting combination : : : : : : : : : : : : : : : : : : : : : : : : 15 2.2 Collocation for BVP in DAE with invariants : : : : : : : : : : : : : : : : : 17 2.2.1 DAE models from mechanics : : : : : : : : : : : : : : : : : : : : : : 17 2.2.2 Collocation discretization of two point BVP in DAE : : : : : : :
A Merit Function for Inequality Constrained Nonlinear Programming Problems
 Internal Report 4702, National Institute of Standards and Technology
, 1993
"... We consider the use of the sequential quadratic programming (SQP) technique for solving the inequality constrained minimization problem min x f(x) subject to: g i (x) 0; i = 1; : : : ; m: SQP methods require the use of an auxiliary function, called a merit function or linesearch function, for asse ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
We consider the use of the sequential quadratic programming (SQP) technique for solving the inequality constrained minimization problem min x f(x) subject to: g i (x) 0; i = 1; : : : ; m: SQP methods require the use of an auxiliary function, called a merit function or linesearch function, for assessing the steps that are generated. We derive a merit function by adding slack variables to create an equality constrained problem and then using the merit function developed earlier by the authors for the equality constrained case. We stress that we do not solve the slack variable problem, but only use it to construct the merit function. The resulting function is simplified in a certain way that leads to an effective procedure for updating the squares of the slack variables. A globally convergent algorithm, based on this merit function, is suggested, and is demonstrated to be effective in practice. Contribution of the National Institute of Standards and Technology and not subject to copyr...
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 ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
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.
A Piecewise LineSearch Technique for Maintaining the Positive Definiteness of the Matrices in the SQP Method
, 1997
"... Abstract. A technique for maintaining the positive definiteness of the matrices in the quasiNewton version of the SQP algorithm is proposed. In our algorithm, matrices approximating the Hessian of the augmented Lagrangian are updated. The positive definiteness of these matrices in the space tangent ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Abstract. A technique for maintaining the positive definiteness of the matrices in the quasiNewton version of the SQP algorithm is proposed. In our algorithm, matrices approximating the Hessian of the augmented Lagrangian are updated. The positive definiteness of these matrices in the space tangent to the constraint manifold is ensured by a socalled piecewise linesearch technique, while their positive definiteness in a complementary subspace is obtained by setting the augmentation parameter. In our experiment, the combination of these two ideas leads to a new algorithm that turns out to be more robust and often improves the results obtained with other approaches.