The piecewise linear optimization polytope: new inequalities and intersection with semi-continuous constraints

2012 ◽  
Vol 141 (1-2) ◽  
pp. 217-255 ◽  
Author(s):  
Ming Zhao ◽  
Ismael Regis de Farias
Keyword(s):  
Piecewise Linear ◽  
Linear Optimization ◽  
Continuous Constraints ◽  
New Inequalities

scholarly journals A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Hamid Reza Erfanian ◽  
M. H. Noori Skandari ◽  
A. V. Kamyad
Keyword(s):  
Nonsmooth Optimization ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Piecewise Linear Function ◽  
Nonsmooth Equations ◽  
Smooth Functions ◽  
Generalized Derivative ◽  
Novel Approach

We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other words, nonsmooth function is approximated by a piecewise linear function based on generalized derivative. In the next step, we solve smooth linear optimization problem whose optimal solution is an approximate solution of main problem. Then, we apply the results for solving system of nonsmooth equations. Finally, for efficiency of our approach some numerical examples have been presented.

Piecewise linear optimization

Computing ◽  
1980 ◽  
Vol 25 (1) ◽  
pp. 59-76 ◽  
Author(s):  
J. K. Brunner
Keyword(s):  
Piecewise Linear ◽  
Linear Optimization

Discontinuous piecewise linear optimization

1998 ◽  
Vol 80 (3) ◽  
pp. 315-380 ◽  
Author(s):  
Andrew R. Conn ◽  
Marcel Mongeau
Keyword(s):  
Piecewise Linear ◽  
Linear Optimization

scholarly journals Nonconvex, lower semicontinuous piecewise linear optimization

2008 ◽  
Vol 5 (2) ◽  
pp. 467-488 ◽  
Author(s):  
Juan Pablo Vielma ◽  
Ahmet B. Keha ◽  
George L. Nemhauser
Keyword(s):  
Piecewise Linear ◽  
Lower Semicontinuous ◽  
Linear Optimization
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