Abstract. In this paper we introduce a new approach to solve constrained nonlinear nonsmooth programming problems with any desirable accuracy even when the objective function is a non-smooth one. In this approach for any given desirable accuracy, all the nonlinear functions of original problem (in objective function and in constraints) are approximated by a piecewise linear functions. We then represent an efficient algorithm to find the global solution of the later problem. The obtained solution has desirable accuracy and the error is completely controllable.One of the main advantages of our approach is that the approach can be extended to problems with non-smooth structure by introducing a novel definition of Global Weak Differentiation in the sense of L 1 norm. Finally some numerical examples are given to show the efficiency of the proposed approach to solve approximately constraints nonlinear non-smooth programming problems.Mathematical subject classification: 90C30, 49M37, 49M25.

In this paper a new approach for obtaining an approximation global optimum solution of zero-one nonlinear programming (0-1 NP) problem which we call it Parametric Linearization Approach (P.L.A) is proposed. By using this approach the problem is transformed to a sequence of linear programming problems. The approximately solution of the original 0-1 NP problem is obtained based on the optimum values of the objective functions of this sequence of linear programming problems defined by (P.L.A).

This article proposes a new and efficient iterative procedure to solve a class of discrete-time nonlinear optimal control problems. Based on the Pontryagin's maximum principle, the necessary optimality conditions are formulated in the form of a nonlinear discrete boundary value problem (BVP). This problem is then reduced into a sequence of linear discrete BVPs by applying a series expansion approach called the modal series method. Solving the aforementioned sequence by using the techniques of solving linear difference equations, the optimal control law is derived in the form of a uniformly convergent series. In order to demonstrate the efficiency of the proposed method in practice, an iterative algorithm with a fast rate of convergence is provided. In a recursive manner, only a few iterations are needed to find a suboptimal control law with enough accuracy. The effectiveness of this new technique is verified by solving some numerical examples.