Abstract
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.
Highlights
Many problems of considerable practical importance can be related to the solution of nonsmooth optimization of problems (NSOPs) and system of nonsmooth equations
The focus of this paper is the numerical solution of NSOPs and system of nonsmooth equations
We describe a class of approximations which are constructed as piecewise linear functions based on generalized derivative (GD) of nonsmooth functions
Summary
Many problems of considerable practical importance can be related to the solution of nonsmooth optimization of problems (NSOPs) and system of nonsmooth equations. Optimization a function is one of the most important problems of real life and plays a fundamental role in mathematics and its applications in the other disciplines such as control theory, optimal control, engineering, and economics. Nonsmooth optimization refers to the more general problem of minimizing functions that are typically not differentiable at their minimizers. The focus of this paper is the numerical solution of NSOPs and system of nonsmooth equations. The techniques for solving the minimization problems and nonsmooth equations are closely related.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
