5,411 research outputs found
On the resolution of the generalized nonlinear complementarity problem
Minimization of a differentiable function subject to box constraints is proposed as a strategy to solve the generalized nonlinear complementarity problem ( GNCP) defined on a polyhedral cone. It is not necessary to calculate projections that complicate and sometimes even disable the implementation of algorithms for solving these kinds of problems. Theoretical results that relate stationary points of the function that is minimized to the solutions of the GNCP are presented. Perturbations of the GNCP are also considered, and results are obtained related to the resolution of GNCPs with very general assumptions on the data. These theoretical results show that local methods for box-constrained optimization applied to the associated problem are efficient tools for solving the GNCP. Numerical experiments are presented that encourage the use of this approach.Minimization of a differentiable function subject to box constraints is proposed as a strategy to solve the generalized nonlinear complementarity problem ( GNCP) defined on a polyhedral cone. It is not necessary to calculate projections that complicate an122303321CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOsem informaçãosem informaçã
Hybrid Newton-type method for a class of semismooth equations
In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite-difference Newton method to an inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear or quadratic. We report also several numerical results obtained applying the method to suitable reformulations of well-known nonlinear complementarity problem
Tolling, Capacity Selection and Equilibrium Problems with Equilibrium Constraints
An Equilibrium problem with an equilibrium constraint is a mathematical construct that can be applied to private competition in highway networks. In this paper we consider the problem of finding a Nash Equilibrium regarding competition in toll pricing on a network utilising 2 alternative algorithms. In the first algorithm, we utilise a Gauss Siedel fixed point approach based on the cutting constraint algorithm for toll pricing. In the second algorithm, we extend an existing sequential linear complementarity approach for finding Nash equilibrium subject to Wardrop Equilibrium constraints. Finally we consider how the equilibrium may change between the Nash competitive equilibrium and a collusive equilibrium where the two players co-operate to form the equivalent of a monopoly operation
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
Stable Prehensile Pushing: In-Hand Manipulation with Alternating Sticking Contacts
This paper presents an approach to in-hand manipulation planning that
exploits the mechanics of alternating sticking contact. Particularly, we
consider the problem of manipulating a grasped object using external pushes for
which the pusher sticks to the object. Given the physical properties of the
object, frictional coefficients at contacts and a desired regrasp on the
object, we propose a sampling-based planning framework that builds a pushing
strategy concatenating different feasible stable pushes to achieve the desired
regrasp. An efficient dynamics formulation allows us to plan in-hand
manipulations 100-1000 times faster than our previous work which builds upon a
complementarity formulation. Experimental observations for the generated plans
show that the object precisely moves in the grasp as expected by the planner.
Video Summary -- youtu.be/qOTKRJMx6HoComment: IEEE International Conference on Robotics and Automation 201
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