Results 11  20
of
269
An Algorithm for Nonlinear Optimization Using Linear Programming and Equality Constrained Subproblems
, 2003
"... This paper describes an activeset algorithm for largescale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the activ ..."
Abstract

Cited by 41 (12 self)
 Add to MetaCart
This paper describes an activeset algorithm for largescale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained by making a linear approximation to the ` 1 penalty function inside a trust region. In the second stage, an equality constrained quadratic program (EQP) is solved involving only those constraints that are active at the solution of the linear program.
Modifying SQP for degenerate problems
 Preprint ANL/MCSP6991097, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill
, 1997
"... Abstract. Most local convergence analyses of the sequential quadratic programming (SQP) algorithm for nonlinear programming make strong assumptions about the solution, namely, that the active constraint gradients are linearly independent and that there are no weakly active constraints. In this paper ..."
Abstract

Cited by 39 (5 self)
 Add to MetaCart
Abstract. Most local convergence analyses of the sequential quadratic programming (SQP) algorithm for nonlinear programming make strong assumptions about the solution, namely, that the active constraint gradients are linearly independent and that there are no weakly active constraints. In this paper, we establish a framework for variants of SQP that retain the characteristic superlinear convergence rate even when these assumptions are relaxed, proving general convergence results and placing some recently proposed SQP variants in this framework. We discuss the reasons for which implementations of SQP often continue to exhibit good local convergence behavior even when the assumptions commonly made in the analysis are violated. Finally, we describe a new algorithm that formalizes and extends standard SQP implementation techniques, and we prove convergence results for this method also. AMS subject classifications. 90C33, 90C30, 49M45 1. Introduction. We
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 ..."
Abstract

Cited by 38 (11 self)
 Add to MetaCart
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.
KNITRO: An integrated package for nonlinear optimization
 Large Scale Nonlinear Optimization, 35–59, 2006
, 2006
"... This paper describes Knitro 5.0, a Cpackage for nonlinear optimization that combines complementary approaches to nonlinear optimization to achieve robust performance over a wide range of application requirements. The package is designed for solving largescale, smooth nonlinear programming problems ..."
Abstract

Cited by 38 (3 self)
 Add to MetaCart
This paper describes Knitro 5.0, a Cpackage for nonlinear optimization that combines complementary approaches to nonlinear optimization to achieve robust performance over a wide range of application requirements. The package is designed for solving largescale, smooth nonlinear programming problems, and it is also effective for the following special cases: unconstrained optimization, nonlinear systems of equations, least squares, and linear and quadratic programming. Various algorithmic options are available, including two interior methods and an activeset method. The package provides crossover techniques between algorithmic options as well as automatic selection of options and settings. 1
Momentumbased Parameterization of Dynamic Character Motion
, 2004
"... This paper presents a system for rapid editing of highly dynamic motion capture data. At the heart of this system is an optimization algorithm that can transform the captured motion so that it satisfies highlevel user constraints while enforcing that the linear and angular momentum of the motion ..."
Abstract

Cited by 37 (2 self)
 Add to MetaCart
This paper presents a system for rapid editing of highly dynamic motion capture data. At the heart of this system is an optimization algorithm that can transform the captured motion so that it satisfies highlevel user constraints while enforcing that the linear and angular momentum of the motion remain physically plausible. Unlike most previous approaches to motion editing, our algorithm does not require pose specification or model reduction, and the user only need specify highlevel changes to the input motion. To preserve the dynamic behavior of the input motion, we introduce a splinebased parameterization that matches the linear and angular momentum patterns of the motion capture data. Because our algorithm enables rapid convergence by presenting a good initial state of the optimization, the user can efficiently generate a large number of realistic motions from a single input motion. The algorithm
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 35 (8 self)
 Add to MetaCart
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...
Optimal gait and form for animal locomotion
 ACM Transactions on Graphics
, 2009
"... We present a fully automatic method for generating gaits and morphologies for legged animal locomotion. Given a specific animal’s shape we can determine an efficient gait with which it can move. Similarly, we can also adapt the animal’s morphology to be optimal for a specific locomotion task. We sho ..."
Abstract

Cited by 25 (2 self)
 Add to MetaCart
We present a fully automatic method for generating gaits and morphologies for legged animal locomotion. Given a specific animal’s shape we can determine an efficient gait with which it can move. Similarly, we can also adapt the animal’s morphology to be optimal for a specific locomotion task. We show that determining such gaits is possible without the need to specify a good initial motion, and without manually restricting the allowed gaits of each animal. Our approach is based on a hybrid optimization method which combines an efficient derivativeaware spacetime constraints optimization with a derivativefree approach able to find nonlocal solutions in highdimensional discontinuous spaces. We demonstrate the effectiveness of this approach by synthesizing dynamic locomotions of bipeds, a quadruped, and an imaginary fivelegged creature.
LQRTrees: Feedback motion planning via sums of squares verification
 International Journal of Robotics Research
, 2010
"... Advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of attraction for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses rigorously computed stability regions to build a sparse tree ..."
Abstract

Cited by 22 (8 self)
 Add to MetaCart
Advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of attraction for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses rigorously computed stability regions to build a sparse tree of LQRstabilized trajectories. The region of attraction of this nonlinear feedback policy “probabilistically covers ” the entire controllable subset of the state space, verifying that all initial conditions that are capable of reaching the goal will reach the goal. We numerically investigate the properties of this systematic nonlinear feedback design algorithm on simple nonlinear systems, prove the property of probabilistic coverage, and discuss extensions and implementation details of the basic algorithm. 1
Interior methods for mathematical programs with complementarity constraints
 SIAM J. Optim
, 2004
"... This paper studies theoretical and practical properties of interiorpenalty methods for mathematical programs with complementarity constraints. A framework for implementing these methods is presented, and the need for adaptive penalty update strategies is motivated with examples. The algorithm is sh ..."
Abstract

Cited by 22 (8 self)
 Add to MetaCart
This paper studies theoretical and practical properties of interiorpenalty methods for mathematical programs with complementarity constraints. A framework for implementing these methods is presented, and the need for adaptive penalty update strategies is motivated with examples. The algorithm is shown to be globally convergent to strongly stationary points, under standard assumptions. These results are then extended to an interiorrelaxation approach. Superlinear convergence to strongly stationary points is also established. Two strategies for updating the penalty parameter are proposed, and their efficiency and robustness are studied on an extensive collection of test problems.
A globally convergent linearly constrained Lagrangian method for nonlinear optimization
 SIAM J. Optim
, 2002
"... Abstract. For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form “minimize an augmented Lagrangian function subject to linearized constraints. ” Such methods converge rapidly near a solution but may not be relia ..."
Abstract

Cited by 22 (5 self)
 Add to MetaCart
Abstract. For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form “minimize an augmented Lagrangian function subject to linearized constraints. ” Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. Nevertheless, the wellknown software package MINOS has proved effective on many large problems. Its success motivates us to derive a related LCL algorithm that possesses three important properties: it is globally convergent, the subproblem constraints are always feasible, and the subproblems may be solved inexactly. The new algorithm has been implemented in Matlab, with an option to use either MINOS or SNOPT (Fortran codes) to solve the linearly constrained subproblems. Only first derivatives are required. We present numerical results on a subset of the COPS, HS, and CUTE test problems, which include many large examples. The results demonstrate the robustness and efficiency of the stabilized LCL procedure.