In this paper, we define a functional optimization problem corresponding to smooth functions which its optimal solution is first derivative of these functions in a domain. These functional optimization problems are ap...In this paper, we define a functional optimization problem corresponding to smooth functions which its optimal solution is first derivative of these functions in a domain. These functional optimization problems are applied for non-smooth functions which by solving these problems we obtain a kind of generalized first derivatives. For this purpose, a linear programming problem corresponding functional optimization problem is obtained which their optimal solutions give the approximate generalized first derivative. We show the efficiency of our approach by obtaining derivative and generalized derivative of some smooth and nonsmooth functions respectively in some illustrative examples.展开更多
In this paper, a new approach using linear combination property of intervals and discretization is proposed to solve a class of nonlinear optimal control problems, containing a nonlinear system and linear functional, ...In this paper, a new approach using linear combination property of intervals and discretization is proposed to solve a class of nonlinear optimal control problems, containing a nonlinear system and linear functional, in three phases. In the first phase, using linear combination property of intervals, changes nonlinear system to an equivalent linear system, in the second phase, using discretization method, the attained problem is converted to a linear programming problem, and in the third phase, the latter problem will be solved by linear programming methods. In addition, efficiency of our approach is confirmed by some numerical examples.展开更多
In this paper, we propose a new approach for a class of optimal control problems governed by Volterra integral equations which is based on linear combination property of intervals. We convert the nonlinear terms in co...In this paper, we propose a new approach for a class of optimal control problems governed by Volterra integral equations which is based on linear combination property of intervals. We convert the nonlinear terms in constraints of problem to the corresponding linear terms. Discretization method is also applied to convert the new problems to the discrete-time problem. In addition, some numerical examples are presented to illustrate the effectiveness of the proposed approach.展开更多
文摘In this paper, we define a functional optimization problem corresponding to smooth functions which its optimal solution is first derivative of these functions in a domain. These functional optimization problems are applied for non-smooth functions which by solving these problems we obtain a kind of generalized first derivatives. For this purpose, a linear programming problem corresponding functional optimization problem is obtained which their optimal solutions give the approximate generalized first derivative. We show the efficiency of our approach by obtaining derivative and generalized derivative of some smooth and nonsmooth functions respectively in some illustrative examples.
文摘In this paper, a new approach using linear combination property of intervals and discretization is proposed to solve a class of nonlinear optimal control problems, containing a nonlinear system and linear functional, in three phases. In the first phase, using linear combination property of intervals, changes nonlinear system to an equivalent linear system, in the second phase, using discretization method, the attained problem is converted to a linear programming problem, and in the third phase, the latter problem will be solved by linear programming methods. In addition, efficiency of our approach is confirmed by some numerical examples.
文摘In this paper, we propose a new approach for a class of optimal control problems governed by Volterra integral equations which is based on linear combination property of intervals. We convert the nonlinear terms in constraints of problem to the corresponding linear terms. Discretization method is also applied to convert the new problems to the discrete-time problem. In addition, some numerical examples are presented to illustrate the effectiveness of the proposed approach.
