User's Guide for NPSOL (Version 4.0): A Fortran Package for Nonlinear Programming.

Gill, Philip E.; Murray, Walter; Saunders, Michael A.; Wright, Margaret H.

doi:10.21236/ada169115

Cited by 682 publications

(631 citation statements)

References 2 publications

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“…A reasonable initial tape is generally helpful in avoiding problems with local minima. The resulting optimization problems are also sparse, allowing efficient (locally optimal) solutions with large-scale sparse solvers such as SNOPT [8], and trivial parallel/distributed evaluation of the cost and constraints.…”

Section: Introductionmentioning

confidence: 99%

Direct Trajectory Optimization of Rigid Body Dynamical Systems through Contact

Posa

Tedrake

2013

Springer Tracts in Advanced Robotics

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Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Most state-of-the-art techniques treat the discontinuous dynamics of contact as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning through contact that eliminates the requirement for an a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem (LCP) for forward simulation, the proposed algorithm leverages Sequential Quadratic Programming (SQP) to naturally resolve contact constraint forces while simultaneously optimizing a trajectory and satisfying nonlinear complementarity constraints. The method scales well to high dimensional systems with large numbers of possible modes. We demonstrate the approach using three increasingly complex systems: rotating a pinned object with a finger, planar walking with the Spring Flamingo robot, and high speed bipedal running on the FastRunner platform.

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Section: Introductionmentioning

confidence: 99%

Direct Trajectory Optimization of Rigid Body Dynamical Systems through Contact

Posa

Tedrake

2013

Springer Tracts in Advanced Robotics

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“…All QPs are solved using TOMLAB CPLEX version 7.0 (R7.0.0) (see [32]) with the Primal Simplex option, which preliminary studies indicate result in the smallest QP run time. We also examined the LSSOL QP solver (see [33]), but its run times appear inferior to that of CPLEX for large-scale QPs arising in the present context. Algorithm 2.1 of [6] is implemented in the solver CFSQP [34] and we have verified that our MATLAB implementation of that algorithm produces comparable results in terms of number of iterations and run time as CFSQP.…”

Section: Numerical Resultsmentioning

confidence: 99%

On Solving Large-Scale Finite Minimax Problems Using Exponential Smoothing

Pee

Røyset

2010

J Optim Theory Appl

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This paper focuses on finite minimax problems with many functions, and their solution by means of exponential smoothing. We conduct run-time complexity and rate of convergence analysis of smoothing algorithms and compare them with those of SQP algorithms. We find that smoothing algorithms may have only sublinear rate of convergence, but as shown by our complexity results, their slow rate of convergence may be compensated by small computational work per iteration. We present two smoothing algorithms with active-set strategies and novel precision-parameter adjustment schemes. Numerical results indicate that the algorithms are competitive with other algorithms from the literature, and especially so when a large number of functions are nearly active at stationary points.

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“…These solvers generally perform quite well in practice. Many systems designed for smooth nonconvex NLPs will often solve smooth CPs efficiently as well [32,69,112,70,41,31,156,122,14,33,13,71,61,1531. This is not surprising when one considers that these algorithms typically exploit local convexity when computing search directions.…”

Section: Smooth Convex Programsmentioning

confidence: 99%