A New Low Rank Quasi-Newton Update Scheme for Nonlinear Programming

Fletcher, R.

doi:10.1007/0-387-33006-2_25

Cited by 6 publications

(7 citation statements)

References 10 publications

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“…As long as the second order information is positive definite we will converge at least linearly. However, it would be desirable to either directly update H or even its decomposition R like in [21] in order to improve the convergence behaviour and save computation time.…”

Section: Discussionmentioning

confidence: 99%

Singularity Resolution in Equality and Inequality Constrained Hierarchical Task-Space Control by Adaptive Nonlinear Least Squares

Pfeiffer¹,

Escande²,

Kheddar³

2018

IEEE Robot. Autom. Lett.

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We propose a robust method to handle kinematic and algorithmic singularities of any kinematically redundant robot under task-space hierarchical control with ordered equalities and inequalities. Our main idea is to exploit a second order model of the non-linear kinematic function, in the sense of the Newton's method in optimization. The second order information is provided by a hierarchical BFGS algorithm omitting the heavy computation required for the true Hessian. In the absence of singularities, which is robustly detected, we use the Gauss-Newton algorithm that has quadratic convergence. In all cases we keep a least-squares formulation enabling good computation performances. Our approach is demonstrated in simulation with a simple robot and a humanoid robot, and compared to state-of-the-art algorithms.

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Section: Discussionmentioning

confidence: 99%

Singularity Resolution in Equality and Inequality Constrained Hierarchical Task-Space Control by Adaptive Nonlinear Least Squares

Pfeiffer¹,

Escande²,

Kheddar³

2018

IEEE Robot. Autom. Lett.

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“…When H k is low rank, or diagonal plus low rank, the method is practical even for large values of n. (Such methods are often called limited memory, since they do not require the storage of an n × n matrix.) For OSMM we propose to use the low-rank quasi-Newton choice given in [23], described in detail in §A.1. We can express H k as…”

Section: Approximation Of the Oracle Functionmentioning

confidence: 99%

Minimizing Oracle-Structured Composite Functions

Shen

Ali

Boyd

2021

Preprint

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We consider the problem of minimizing a composite convex function with two different access methods: an oracle, for which we can evaluate the value and gradient, and a structured function, which we access only by solving a convex optimization problem. We are motivated by two associated technological developments. For the oracle, systems like PyTorch or TensorFlow can automatically and efficiently compute gradients, given a computation graph description. For the structured function, systems like CVXPY accept a high level domain specific language description of the problem, and automatically translate it to a standard form for efficient solution. We develop a method that makes minimal assumptions about the two functions, does not require the tuning of algorithm parameters, and works well in practice across a variety of problems. Our algorithm combines a number of well-known ideas, including a low-rank quasi-Newton approximation of curvature, piecewise affine lower bounds from bundle-type methods, and two types of damping to ensure stability. We illustrate the method on stochastic optimization, utility maximization, and risk-averse programming problems.

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“…Finally, we tried a mixed BFGS-SR1 scheme [24], but we did not get good results with it. The above formulas approximate directly the Hessian of L. Another approach is to use them to approximate individually the Hessian matrices of the cost function f and of every constraints c i , before using the fact that ∇…”

Section: Hessian Computationmentioning

confidence: 99%

Multicontact Postures Computation on Manifolds

2018

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Abstract-We propose a framework to generate static robot configurations satisfying a set of physical and geometrical constraints. This is done by formulating nonlinear constrained optimization problems over non-Euclidean manifolds and solving them. To do so, we present a new sequential quadratic programming (SQP) solver working natively on general manifolds, and propose an interface to easily formulate the problems, with the tedious and error-prone work automated for the user. We also introduce several new types of constraints for having more complex contacts or working on forces/torques. Our approach allows an elegant mathematical description of the constraints and we exemplify it through formulation and computation examples in complex scenarios with humanoid robots.

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A New Low Rank Quasi-Newton Update Scheme for Nonlinear Programming

Cited by 6 publications

References 10 publications

Singularity Resolution in Equality and Inequality Constrained Hierarchical Task-Space Control by Adaptive Nonlinear Least Squares

Singularity Resolution in Equality and Inequality Constrained Hierarchical Task-Space Control by Adaptive Nonlinear Least Squares

Minimizing Oracle-Structured Composite Functions

Multicontact Postures Computation on Manifolds

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