In this paper, we propose a method for finding the best piecewise linearization of nonlinear functions. For this aim, we try to obtain the best approximation of a nonlinear function as a piecewise linear function. Our method is based on an optimization problem. The optimal solution of this optimization problem is the best piecewise linear approximation of nonlinear function. Finally, we examine our method to some examples.
In this paper, we introduce a new approach to obtain a novel numerical solution of fuzzy initial value problem (FIVP). This technique is based on optimization problem. In fact, the optimal solution of optimization problem is approximated solution of fuzzy initial value problem. Theoretical consideration is discussed and some examples are presented to show the ability of the method for fuzzy initial value problem.
In this paper, we introduce a new approach to obtain a novel numerical solution of nonlinear programming problems (NLP) which the objective function (functions) or constraint function (functions) are non-smooth ones. This technique is based on a new piecewise linearization approach. In fact, we transfer the nonlinear programming problem (NLP) to a variational problem that would reduce the new approximated problem to a linear programming problem (LP). Then, the approximated solution of the original problem would be obtained by the LP problem. Finally, numerical examples are given to show the efficiency of the proposed approach.
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