Title :
A New Smooth Method for the l1 Exact Penalty Function for Inequality Constrained Optimization
Author :
Wang, Zhijie ; Liu, Sanming
Author_Institution :
Sch. of Electr. Eng., Shanghai Dianji Univ., Shanghai, China
Abstract :
Exact penalty function methods for the solution of constrained optimization problem are based on the construction of a function whose unconstrained minimizing points are also solution of the constrained problem. One of the popular exact penalty functions is l1 exact penalty function. However l1 exact penalty function is not a smooth function. In this paper, we propose a new method for smoothing the l1 exact penalty function for inequality constrained optimization. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem, of the nonsmooth penalty problem problem and of the original optimization problem. We develop an efficient algorithm for solving the optimization problem based the smoothed penalty function and prove the convergence of the algorithm.
Keywords :
constraint theory; convergence; error analysis; nonlinear programming; algorithm convergence; error estimation; exact penalty function method; inequality constrained optimization; optimal objective function values; smoothing method; Approximation algorithms; Constraint optimization; Error analysis; Helium; Mathematics; Physics computing; Smoothing methods; approximation algorithm; l1 exact penalty function; smoothing method;
Conference_Titel :
Computational Science and Optimization (CSO), 2010 Third International Joint Conference on
Conference_Location :
Huangshan, Anhui
Print_ISBN :
978-1-4244-6812-6
Electronic_ISBN :
978-1-4244-6813-3
DOI :
10.1109/CSO.2010.157