scholarly journals Best ellipsoidal relaxation to solve a nonconvex problem

2004 ◽  
Vol 162 (1) ◽  
pp. 183-191
Author(s):  
Souad El Bernoussi
Keyword(s):  
Nonconvex Problem

Influence of End-Effector Velocities on Robotic Manipulator Dynamic Performance: An Analytical Approach

2003 ◽  
Author(s):  
ChangHwan Kim ◽  
Alan Bowling
Keyword(s):  
Quadratic Forms ◽  
Dynamic Performance ◽  
Optimal Solution ◽  
Problem Formulation ◽  
Optimization Techniques ◽  
Curve Analysis ◽  
Centrifugal Forces ◽  
End Effector ◽  
Nonconvex Problem ◽  
Torque Curve

This article explores the effect that end-effector velocities have on a nonredundant robotic manipulator’s ability to accelerate its end-effector as well as to apply forces/moments to the environment at the end-effector. The velocity effects considered here are the Coriolis and Centrifugal forces, and the reduction of actuator torque with rotor velocity, as described by the speed-torque curve. Analysis of these effects is accomplished using optimization techniques, where the problem formulation consists of a cost function and constraints which are all purely quadratic forms, yielding a nonconvex problem. An analytical solution, based on the dialytic elimination technique, is developed which guarantees that the globally optimal solution can be found. The PUMA 560 manipulator is used as an example to illustrate this methodology.

Analysis of a Nonconvex Problem Related to Signal Selective Smoothing

1997 ◽  
Vol 07 (03) ◽  
pp. 313-328 ◽  
Author(s):  
M. Chipot ◽  
R. March ◽  
M. Rosati ◽  
G. Vergara Caffarelli
Keyword(s):  
Variational Problem ◽  
Existence Result ◽  
Minimizing Sequences ◽  
Qualitative Properties ◽  
Nonconvex Problem ◽  
Nonconvex Variational Problem ◽  
Selective Smoothing

We study some properties of a nonconvex variational problem. We fail to attain the infimum of the functional that has to be minimized. Instead, minimizing sequences develop gradient oscillations which allow them to reduce the value of the functional. We show an existence result for a perturbed nonconvex version of the problem, and we study the qualitative properties of the corresponding minimizer. The pattern of the gradient oscillations for the original nonperturbed problem is analyzed numerically.

scholarly journals An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

2013 ◽  
Vol 23 (2) ◽  
pp. 263-276 ◽  
Author(s):  
Mikaël Barboteu ◽  
Krzysztof Bartosz ◽  
Piotr Kalita
Keyword(s):  
Contact Problem ◽  
Frictional Contact ◽  
Numerical Approach ◽  
Bundle Method ◽  
Nonconvex Problem ◽  
Proximal Bundle Method ◽  
Loss Of Contact ◽  
The Galerkin Method ◽  
Bilateral Contact ◽  
Numerical Approaches

We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.

scholarly journals A Branch-and-Reduce Approach for Solving Generalized Linear Multiplicative Programming

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Chun-Feng Wang ◽  
San-Yang Liu ◽  
Geng-Zhong Zheng
Keyword(s):  
Linear Programming ◽  
Linearization Method ◽  
Multiplicative Programming ◽  
Nonconvex Problem ◽  
Linear Multiplicative Programming ◽  
Linear Programming Problems ◽  
Overall Performance ◽  
Approximate Linearization

We consider a branch-and-reduce approach for solving generalized linear multiplicative programming. First, a new lower approximate linearization method is proposed; then, by using this linearization method, the initial nonconvex problem is reduced to a sequence of linear programming problems. Some techniques at improving the overall performance of this algorithm are presented. The proposed algorithm is proved to be convergent, and some experiments are provided to show the feasibility and efficiency of this algorithm.

scholarly journals Solution to an Optimal Control Problem via Canonical Dual Method

2009 ◽  
Vol 2009 ◽  
pp. 1-5 ◽  
Author(s):  
Jinghao Zhu ◽  
Jiani Zhou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Analytic Solution ◽  
Dual Method ◽  
Cost Functional ◽  
Nonconvex Problem ◽  
Pontryagin Principle ◽  
Dual Variables ◽  
The Cost

The analytic solution to an optimal control problem is investigated using the canonical dual method. By means of the Pontryagin principle and a transformation of the cost functional, the optimal control of a nonconvex problem is obtained. It turns out that the optimal control can be expressed by the costate via canonical dual variables. Some examples are illustrated.

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