Complementarity condition

2011 ◽  
Keyword(s):  
Complementarity Condition

3-1 Piecewise NCP Function for New Nonmonotone QP-Free Infeasible Method

2014 ◽  
Vol 26 (5) ◽  
pp. 566-572 ◽  
Author(s):  
Ailan Liu ◽  
◽  
Dingguo Pu ◽  
◽  
Keyword(s):  
Constraint Qualification ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Ncp Function ◽  
Line Searches ◽  
Complementarity Condition ◽  
Linear Independence Constraint Qualification ◽  
Systems Of Linear Equations

<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00260005/04.jpg"" width=""300"" />Algorithm flow chart</div> We propose a nonmonotone QP-free infeasible method for inequality-constrained nonlinear optimization problems based on a 3-1 piecewise linear NCP function. This nonmonotone QP-free infeasible method is iterative and is based on nonsmooth reformulation of KKT first-order optimality conditions. It does not use a penalty function or a filter in nonmonotone line searches. This algorithm solves only two systems of linear equations with the same nonsingular coefficient matrix, and is implementable and globally convergent without a linear independence constraint qualification or a strict complementarity condition. Preliminary numerical results are presented. </span>

AN INFEASIBLE SSLE FILTER ALGORITHM FOR GENERAL CONSTRAINED OPTIMIZATION WITHOUT STRICT COMPLEMENTARITY

2011 ◽  
Vol 28 (03) ◽  
pp. 361-399 ◽  
Author(s):  
CHUNGEN SHEN ◽  
WENJUAN XUE ◽  
DINGGUO PU
Keyword(s):  
Linear Independence ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Active Set ◽  
Strict Complementarity ◽  
Complementarity Condition ◽  
Sequential Systems ◽  
Computational Effect ◽  
Systems Of Linear Equations ◽  
One Step

In this paper, we propose a new sequential systems of linear equations (SSLE) filter algorithm, which is an infeasible QP-free method. The new algorithm needs to solve a few reduced systems of linear equations with the same nonsingular coefficient matrix, and after finitely many iterations, only two linear systems need to be solved. Furthermore, the nearly active set technique is used to improve the computational effect. Under the linear independence condition, the global convergence is proved. In particular, the rate of convergence is proved to be one-step superlinear without assuming the strict complementarity condition. Numerical results and comparison with other algorithms indicate that the new algorithm is promising.

Using an Anti-Relaxation Step to Improve the Accuracy of the Frictional Contact Solution in a DVI Framework for Rigid Body Dynamics

2016 ◽  
Author(s):  
Daniel Melanz ◽  
Hammad Mazhar ◽  
Dan Negrut
Keyword(s):  
Frictional Contact ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Science And Engineering ◽  
Complementarity Condition ◽  
Body Dynamics ◽  
Engineering Problems ◽  
The Impact

Systems composed of rigid bodies interacting through frictional contact are manifest in several science and engineering problems. The number of contacts can be small, such as in robotics and geared machinery, or large, such as in terrame-chanics applications, additive manufacturing, farming, food industry, and pharmaceutical industry. Currently, there are two popular approaches for handling the frictional contact problem in dynamic systems. The penalty method calculates the frictional contact force based on the kinematics of the interaction, some representative parameters, and an empirical force law. Alternatively, the complementarity method, based on a differential variational inequality (DVI), enforces non-penetration of rigid bodies via a complementarity condition. This contribution concentrates on the latter approach and investigates the impact of an anti-relaxation step that improves the accuracy of the frictional contact solution. We show that the proposed anti-relaxation step incurs a relatively modest cost to improve the quality of a numerical solution strategy which poses the calculation of the frictional contact forces as a cone-complementarity problem.

scholarly journals A Mixed Line Search Smoothing Quasi-Newton Method for Solving Linear Second-Order Cone Programming Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zhuqing Gui ◽  
Chunyan Hu ◽  
Zhibin Zhu
Keyword(s):  
Nonlinear System ◽  
Newton Method ◽  
Jordan Algebra ◽  
Line Search ◽  
Primal Problem ◽  
First Order ◽  
Second Order Cone ◽  
Complementarity Condition ◽  
Quasi Newton ◽  
Mixed Line

Firstly, we give the Karush-Kuhn-Tucker (KKT) optimality condition of primal problem and introduce Jordan algebra simply. On the basis of Jordan algebra, we extend smoothing Fischer-Burmeister (F-B) function to Jordan algebra and make the complementarity condition smoothing. So the first-order optimization condition can be reformed to a nonlinear system. Secondly, we use the mixed line search quasi-Newton method to solve this nonlinear system. Finally, we prove the globally and locally superlinear convergence of the algorithm.

On the preconditioned projective iterative methods for the linear complementarity problems

2020 ◽  
Vol 54 (2) ◽  
pp. 341-349 ◽  
Author(s):  
Seyyed Ahmad Edalatpanah
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Convergence Properties ◽  
New Approach ◽  
Complementarity Condition ◽  
New Strategy ◽  
Preconditioned Iterative

This paper aims to propose the new preconditioning approaches for solving linear complementarity problem (LCP). Some years ago, the preconditioned projected iterative methods were presented for the solution of the LCP, and the convergence of these methods has been analyzed. However, most of these methods are not correct, and this is because the complementarity condition of the preconditioned LCP is not always equivalent to that of the un-preconditioned original LCP. To overcome this shortcoming, we present a new strategy with a new preconditioner that ensures the solution of the same problem is correct. We also study the convergence properties of the new preconditioned iterative method for solving LCP. Finally, the new approach is illustrated with the help of a numerical example.

Remarks on the complementarity condition in conjugated molecules

1972 ◽  
Vol 4 (16) ◽  
pp. 845-848 ◽  
Author(s):  
M. Giambiagi ◽  
M. S. de Giambiagi
Keyword(s):  
Conjugated Molecules ◽  
Complementarity Condition

QP-Free Method for Nonlinear Programming Problems

2011 ◽  
Vol 467-469 ◽  
pp. 882-887
Author(s):  
Ai Ping Jiang ◽  
Feng Wen Huang
Keyword(s):  
Linear Independence ◽  
Accumulation Point ◽  
Strict Complementarity ◽  
First Order ◽  
Ncp Function ◽  
Complementarity Condition ◽  
Dual Variables ◽  
Primal And Dual ◽  
Weaker Conditions ◽  
Quasi Newton

In this paper, A QP-free feasible method was proposed to obtain the local convergence under some weaker conditions for the minimization of a smooth function subject to smooth inequalities. Based on the solutions of linear systems of equation reformulation of the KKT optimality conditions, this method uses the 3-1 NCP function[1].The method is iterative, which means each iteration can be viewed as a perturbation of a Newton or Quasi Newton on both the primal and dual variables for the solution of the equalities in the KKT first order conditions of optimality, and the feasibility of all iterations is ensured in this method. In particular, this method is implementable and globally convergent without assuming the strict complementarity condition, the isolation of the accumulation point and the linear independence of the gradients of active constrained functions. The method has also superlinear convergence rate under some mild conditions.

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