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On the implementation of an algorithm for largescale equality constrained optimization
 SIAM Journal on Optimization
, 1998
"... Abstract. This paper describes a software implementation of Byrd and Omojokun’s trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques ..."
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Cited by 38 (11 self)
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Abstract. This paper describes a software implementation of Byrd and Omojokun’s trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques for solving the subproblems occurring in the algorithm. Second derivative information can be used, but when it is not available, limited memory quasiNewton approximations are made. The performance of the code is studied using a set of difficult test problems from the CUTE collection.
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 35 (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...
On InteriorPoint Newton Algorithms For Discretized Optimal Control Problems With State Constraints
 OPTIM. METHODS SOFTW
, 1998
"... In this paper we consider a class of nonlinear programming problems that arise from the discretization of optimal control problems with bounds on both the state and the control variables. For this class of problems, we analyze constraint qualifications and optimality conditions in detail. We derive ..."
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Cited by 7 (2 self)
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In this paper we consider a class of nonlinear programming problems that arise from the discretization of optimal control problems with bounds on both the state and the control variables. For this class of problems, we analyze constraint qualifications and optimality conditions in detail. We derive an affinescaling and two primaldual interiorpoint Newton algorithms by applying, in an interiorpoint way, Newton's method to equivalent forms of the firstorder optimality conditions. Under appropriate assumptions, the interiorpoint Newton algorithms are shown to be locally welldefined with a qquadratic rate of local convergence. By using the structure of the problem, the linear algebra of these algorithms can be reduced to the null space of the Jacobian of the equality constraints. The similarities between the three algorithms are pointed out, and their corresponding versions for the general nonlinear programming problem are discussed.
A Global Convergence Theory for a General Class of TrustRegionBased Algorithms for Constrained Optimization Without Assuming Regularity
 SIAM Journal on Optimization
, 1997
"... This work presents a convergence theory for a general class of trustregionbased algorithms for solving the smooth nonlinear programming problem with equality constraints. The results are proved under very mild conditions on the quasinormal and tangential components of the trial steps. The Lagrang ..."
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Cited by 3 (0 self)
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This work presents a convergence theory for a general class of trustregionbased algorithms for solving the smooth nonlinear programming problem with equality constraints. The results are proved under very mild conditions on the quasinormal and tangential components of the trial steps. The Lagrange multiplier estimates and the Hessian estimates are assumed to be bounded. In addition, the regularity assumption is not made. In particular, the linear independence of the gradients of the constraints is not assumed. The theory proves global convergence for the class. In particular, it shows that a subsequence of the iteration sequence satisfies one of four types of MayerBliss stationary conditions in the limit. This theory holds for Dennis, ElAlem, and Maciel's class of trustregionbased algorithms. Key Words: Nonlinear programming, equality constrained problems, constrained optimization, global convergence, regularity assumption, augmented Lagrangian, MayerBliss points, stationary p...
Design Issues in Algorithms for Large Scale Nonlinear Programming
, 1999
"... Design Issues in Algorithms for Large Scale Nonlinear Programming Guanghui Liu Ph.D. Supervisor: Jorge Nocedal This dissertation studies a wide range of issues in the design of interior point methods for large scale nonlinear programming. Strategies for computing high quality steps and for rapidly d ..."
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Design Issues in Algorithms for Large Scale Nonlinear Programming Guanghui Liu Ph.D. Supervisor: Jorge Nocedal This dissertation studies a wide range of issues in the design of interior point methods for large scale nonlinear programming. Strategies for computing high quality steps and for rapidly decreasing barrier parameters are introduced. Preconditioning or scaling techniques are developed. To extend the range of applicability of interior methods, feasible variants are proposed, quasiNewton updating methods are introduced, and strategies for the nonmonotone decrease of the merit function are explored. A product of this dissertation is a software, called NITRO, that implements an interior point method using the new algorithmic features presented in this dissertation. The performance of this code is assessed by comparing it with established software for large scale optimization (SNOPT, filterSQP and LOQO). ii ACKNOWLEDGMENT I am grateful to Jorge Nocedal, my PhD supervisor, for i...
NOVEL APPLICATIONS OF OPTIMIZATION TO MOLECULE DESIGN
"... We present results from the application of two conformational search methods: genetic algorithms (GA) and parallel direct search methods for finding all of the low energy conformations of a molecule that are within a certain energy of the global minimum. Genetic algorithms are in a class of biologic ..."
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We present results from the application of two conformational search methods: genetic algorithms (GA) and parallel direct search methods for finding all of the low energy conformations of a molecule that are within a certain energy of the global minimum. Genetic algorithms are in a class of biologically motivated optimization methods that evolve a population of individuals where individuals who are more "fit" have a higher probability of surviving into subsequent generations. The parallel direct search method (PDS) is a type of pattern search method that uses an adaptive grid to search for minima. In addition, we present atechnique for performing energy minimization based on using a constrained optimization method.
Robust Optimal Power Flow Solution Using Trust Region and InteriorPoint Methods
"... Abstract—A globally convergent optimization algorithm for solving large nonlinear optimal power flow (OPF) problems is presented. As power systems become heavily loaded there is an increasing need for globally convergent OPF algorithms. By global convergence one means the optimization algorithm bein ..."
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Abstract—A globally convergent optimization algorithm for solving large nonlinear optimal power flow (OPF) problems is presented. As power systems become heavily loaded there is an increasing need for globally convergent OPF algorithms. By global convergence one means the optimization algorithm being able to converge to an OPF solution, if at least one exists, for any choice of initial point. The globally convergent OPF presented is based on an infinitynorm trust region approach, using interiorpoint methods to solve the trust region subproblems. The performance of the proposed trust region interiorpoint OPF algorithm, when applied to the IEEE 30, 57, 118 and 300bus systems, and to an actual 1211bus system, is compared with that of two widely used nonlinear interiorpoint methods, namely, a pure primaldual and its predictorcorrector variant.