hamid reza erfanian - Academia.edu (original) (raw)

Papers by hamid reza erfanian

Research paper thumbnail of A new approach for a class of optimal control problems of volterra integral equations

In this paper, we propose a new approach for a class of optimal control problems governed by Volt... more 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.

Research paper thumbnail of Optimal Control Of An Hiv Model

Journal of Mathematics and Computer Science

We consider an HIV model, based on optimal control, for identifying the best treatment strategy i... more We consider an HIV model, based on optimal control, for identifying the best treatment strategy in order to maximize the healthy cells by using chemotherapies with minimum side effects. In this paper, a new approach is introduced which transform the constraints of problem to the integral constraints. By an approximation, we obtain a finite dimensional linear programming problem which give us an approximate solution for original problem.

Research paper thumbnail of Approximate Solution Of A Class Of Nonlinear Volterra Integral Equations

Journal of Mathematics and Computer Science

In this paper we introduce an approach by an optimization method to find approximate solution for... more In this paper we introduce an approach by an optimization method to find approximate solution for a class of nonlinear Volterra integral equations of the first and second kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Research paper thumbnail of Estimation method of spatial geostatistical data : Application to rainfall data

International Journal of Advanced Statistics and Probability

Restriction of water resources for agricultural and non-agricultural purposes has caused major di... more Restriction of water resources for agricultural and non-agricultural purposes has caused major difficulties and rainfall is considered as one of the most important water resources. Therefore, predicting rainfall and estimating its rate monthly or annually for each region as one of the most important atmospheric parameters, is of particular importance in optimized usage of water resources.In this paper in addition to the presenting application of novel statistical methods, prediction of rainfall amount has been performed for the entire map of Iran. In this analysis, data of average rainfall of 108 pluviometry stations in different cities of Iran have been used and zoning of rainfall has been prepared for the country.

Research paper thumbnail of Solving a Linear Programming with Fuzzy Constraint and Objective Coefficients

International Journal of Intelligent Systems and Applications, 2016

In this paper, we consider a method for solving a linear programming problem with fu zzy objectiv... more In this paper, we consider a method for solving a linear programming problem with fu zzy objective and coefficient matrix, where the fu zzy numbers are supposed to be triangular. By the proposed method, the Decision Maker will have the flexib ility of choosing. The solving method is based on the Pareto algorith m, which converts the problem to a weightedobjective linear programming. For more illustration, after discussing the problem and the algorith m, we p resent an example, which its solutions are independent from the objective weights.

Research paper thumbnail of Using the Euler-Maruyama Method for Finding a Solution to Stochastic Financial Problems

International Journal of Intelligent Systems and Applications, 2016

The purpose of this paper is to survey stochastic differential equations and Euler-Maruyama metho... more The purpose of this paper is to survey stochastic differential equations and Euler-Maruyama method for appro ximating the solution to these equations in financial p roblems. It is not possible to get explicit solution and analytically answer for many of stochastic differential equations, but in the case of linear stochastic differential equations it may be possible to get an exp licit answer. We can approximate the solution with standard numerical methods, such as Eu ler-Maruyama method, Milstein method and Runge-Kutta method. We will use Eu ler-Maruyama method for simulat ion of stochastic differential equations for financial problems, such as asset pricing model, square-root asset pricing model, payoff for a European call option and estimating value of European call option and Asian option to buy the asset at the future time. We will d iscuss how to find the approximated solutions to stochastic differential equations for financial problems with examples .

Research paper thumbnail of Solving subclass of non-smooth continuous linear and nonlinear programs

In this paper, existence and numerical estimation of the solution of continuous nonlinear program... more In this paper, existence and numerical estimation of the solution of continuous nonlinear programs with weak conditions is discussed. First the original problem to finite number of the subproblems is transformed and then by solving this linear programming problems piecewiseconstant functions is obtained and finally the approximate trajectories of the original one is obtained.

Research paper thumbnail of The optimal method for solving continuous linear and nonlinear programs

Research paper thumbnail of Solving a Class of Separated Continuous Programming Problems Using Linearization and Discretization

In this paper we present a new approach for solving a class of separated con-tinuous programming ... more In this paper we present a new approach for solving a class of separated con-tinuous programming (SCP) problems using convex combination property of intervals. By convex combination property of intervals, we transform the SCP problems to the correspond-ing linear problems. Moreover, discretization method is applied to convert the new problem to a discrete-time problem which we solve it by linear programming methods. Finally, some numerical examples are given to show the efficiency of the proposed approach.

Research paper thumbnail of A New Approach for the Generalized First Derivative and Extension It to the Generalized Second Derivative of Nonsmooth Functions

International Journal of Intelligent Systems and Applications, 2013

In this paper, first derivative of smooth function is defined by the optimal solution of a specia... more In this paper, first derivative of smooth function is defined by the optimal solution of a special optimization problem. In the next step, by using this optimization problem for nonsmooth function, we obtain an approximation for first derivative of nonsmooth function which it is called generalized first derivative. We then extend it to define generalized second derivative for nonsmooth function. Finally, we show the efficiency of our approach by evaluating derivative and generalized first and second derivative of some smooth and nonsmooth functions, respectively.

Research paper thumbnail of Solving subclass of non-smooth continuous linear and nonlinear programs

In this paper, existence and numerical estimation of the solution of continuous nonlinear program... more In this paper, existence and numerical estimation of the solution of continuous nonlinear programs with weak conditions is discussed. First the original problem to finite number of the subproblems is transformed and then by solving this linear programming problems piecewiseconstant functions is obtained and finally the approximate trajectories of the original one is obtained.

Research paper thumbnail of A New Approach for Generalized Partial Derivatives of Non-smooth Functions

ABSTRACT In this paper, we define the functional optimization problems corresponding to multi-var... more ABSTRACT In this paper, we define the functional optimization problems corresponding to multi-variable smooth functions, so that their optimal solutions are partial derivatives of these functions. These functional optimization problems are applied for multi-variables nonsmooth functions, so that by solving these problems we obtain generalized partial derivatives. For this purpose, linear programming problems corresponding to the functional optimization problems are obtained, so that their optimal solutions give the approximate generalized partial derivatives. In some illustrative examples, we show the efficiency of our approach by obtaining the generalized partial derivative of some smooth and nonsmooth functions, respectively.

Research paper thumbnail of Optimal Control of Bone Marrow in Cancer Chemotherapy

Research paper thumbnail of A New Approach for a Class of Optimal Control Problems of Volterra Integral Equations

Intelligent Control and Automation, 2011

In this paper, we propose a new approach for a class of optimal control problems governed by Volt... more 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.

Research paper thumbnail of Control of a class of nonsmooth dynamical systems

Journal of Vibration and Control, 2013

Research paper thumbnail of A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

Journal of Mathematics, 2013

We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth e... more 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.

Research paper thumbnail of A New Definition for Generalized First Derivative of Nonsmooth Functions

Applied Mathematics, 2011

In this paper, we define a functional optimization problem corresponding to smooth functions whic... more 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.

Research paper thumbnail of A numerical approach for nonsmooth ordinary differential equations

Journal of Vibration and Control, 2012

ABSTRACT In this paper, the authors proposed an approach for solving nonsmooth continuous and dis... more ABSTRACT In this paper, the authors proposed an approach for solving nonsmooth continuous and discontinuous ordinary differential equations which is based on a generalization of the Taylor expansion. First is considered a generalized derivative for nonsmooth functions with a single variable which is proposed by Kamyad et al. Then, the generalized Taylor expansion of nonsmooth functions is introduced and used to state an approach. Finally, some numerical examples of nonsmooth ordinary differential equations are solved.

Research paper thumbnail of Solving a Class of Non-Smooth Optimal Control Problems

In this paper, we first propose a new generalized derivative for non-smooth functions and then we... more In this paper, we first propose a new generalized derivative for non-smooth functions and then we utilize this generalized derivative to convert a class of non-smooth optimal control problem to the corresponding smooth form. In the next step, we apply the discretization method to approximate the obtained smooth problem to the nonlinear programming problem. Finally, by solving the last problem, we obtain an approximate optimal solution for main problem.

Research paper thumbnail of A new approach for a class of optimal control problems of volterra integral equations

In this paper, we propose a new approach for a class of optimal control problems governed by Volt... more 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.

Research paper thumbnail of Optimal Control Of An Hiv Model

Journal of Mathematics and Computer Science

We consider an HIV model, based on optimal control, for identifying the best treatment strategy i... more We consider an HIV model, based on optimal control, for identifying the best treatment strategy in order to maximize the healthy cells by using chemotherapies with minimum side effects. In this paper, a new approach is introduced which transform the constraints of problem to the integral constraints. By an approximation, we obtain a finite dimensional linear programming problem which give us an approximate solution for original problem.

Research paper thumbnail of Approximate Solution Of A Class Of Nonlinear Volterra Integral Equations

Journal of Mathematics and Computer Science

In this paper we introduce an approach by an optimization method to find approximate solution for... more In this paper we introduce an approach by an optimization method to find approximate solution for a class of nonlinear Volterra integral equations of the first and second kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Research paper thumbnail of Estimation method of spatial geostatistical data : Application to rainfall data

International Journal of Advanced Statistics and Probability

Restriction of water resources for agricultural and non-agricultural purposes has caused major di... more Restriction of water resources for agricultural and non-agricultural purposes has caused major difficulties and rainfall is considered as one of the most important water resources. Therefore, predicting rainfall and estimating its rate monthly or annually for each region as one of the most important atmospheric parameters, is of particular importance in optimized usage of water resources.In this paper in addition to the presenting application of novel statistical methods, prediction of rainfall amount has been performed for the entire map of Iran. In this analysis, data of average rainfall of 108 pluviometry stations in different cities of Iran have been used and zoning of rainfall has been prepared for the country.

Research paper thumbnail of Solving a Linear Programming with Fuzzy Constraint and Objective Coefficients

International Journal of Intelligent Systems and Applications, 2016

In this paper, we consider a method for solving a linear programming problem with fu zzy objectiv... more In this paper, we consider a method for solving a linear programming problem with fu zzy objective and coefficient matrix, where the fu zzy numbers are supposed to be triangular. By the proposed method, the Decision Maker will have the flexib ility of choosing. The solving method is based on the Pareto algorith m, which converts the problem to a weightedobjective linear programming. For more illustration, after discussing the problem and the algorith m, we p resent an example, which its solutions are independent from the objective weights.

Research paper thumbnail of Using the Euler-Maruyama Method for Finding a Solution to Stochastic Financial Problems

International Journal of Intelligent Systems and Applications, 2016

The purpose of this paper is to survey stochastic differential equations and Euler-Maruyama metho... more The purpose of this paper is to survey stochastic differential equations and Euler-Maruyama method for appro ximating the solution to these equations in financial p roblems. It is not possible to get explicit solution and analytically answer for many of stochastic differential equations, but in the case of linear stochastic differential equations it may be possible to get an exp licit answer. We can approximate the solution with standard numerical methods, such as Eu ler-Maruyama method, Milstein method and Runge-Kutta method. We will use Eu ler-Maruyama method for simulat ion of stochastic differential equations for financial problems, such as asset pricing model, square-root asset pricing model, payoff for a European call option and estimating value of European call option and Asian option to buy the asset at the future time. We will d iscuss how to find the approximated solutions to stochastic differential equations for financial problems with examples .

Research paper thumbnail of Solving subclass of non-smooth continuous linear and nonlinear programs

In this paper, existence and numerical estimation of the solution of continuous nonlinear program... more In this paper, existence and numerical estimation of the solution of continuous nonlinear programs with weak conditions is discussed. First the original problem to finite number of the subproblems is transformed and then by solving this linear programming problems piecewiseconstant functions is obtained and finally the approximate trajectories of the original one is obtained.

Research paper thumbnail of The optimal method for solving continuous linear and nonlinear programs

Research paper thumbnail of Solving a Class of Separated Continuous Programming Problems Using Linearization and Discretization

In this paper we present a new approach for solving a class of separated con-tinuous programming ... more In this paper we present a new approach for solving a class of separated con-tinuous programming (SCP) problems using convex combination property of intervals. By convex combination property of intervals, we transform the SCP problems to the correspond-ing linear problems. Moreover, discretization method is applied to convert the new problem to a discrete-time problem which we solve it by linear programming methods. Finally, some numerical examples are given to show the efficiency of the proposed approach.

Research paper thumbnail of A New Approach for the Generalized First Derivative and Extension It to the Generalized Second Derivative of Nonsmooth Functions

International Journal of Intelligent Systems and Applications, 2013

In this paper, first derivative of smooth function is defined by the optimal solution of a specia... more In this paper, first derivative of smooth function is defined by the optimal solution of a special optimization problem. In the next step, by using this optimization problem for nonsmooth function, we obtain an approximation for first derivative of nonsmooth function which it is called generalized first derivative. We then extend it to define generalized second derivative for nonsmooth function. Finally, we show the efficiency of our approach by evaluating derivative and generalized first and second derivative of some smooth and nonsmooth functions, respectively.

Research paper thumbnail of Solving subclass of non-smooth continuous linear and nonlinear programs

In this paper, existence and numerical estimation of the solution of continuous nonlinear program... more In this paper, existence and numerical estimation of the solution of continuous nonlinear programs with weak conditions is discussed. First the original problem to finite number of the subproblems is transformed and then by solving this linear programming problems piecewiseconstant functions is obtained and finally the approximate trajectories of the original one is obtained.

Research paper thumbnail of A New Approach for Generalized Partial Derivatives of Non-smooth Functions

ABSTRACT In this paper, we define the functional optimization problems corresponding to multi-var... more ABSTRACT In this paper, we define the functional optimization problems corresponding to multi-variable smooth functions, so that their optimal solutions are partial derivatives of these functions. These functional optimization problems are applied for multi-variables nonsmooth functions, so that by solving these problems we obtain generalized partial derivatives. For this purpose, linear programming problems corresponding to the functional optimization problems are obtained, so that their optimal solutions give the approximate generalized partial derivatives. In some illustrative examples, we show the efficiency of our approach by obtaining the generalized partial derivative of some smooth and nonsmooth functions, respectively.

Research paper thumbnail of Optimal Control of Bone Marrow in Cancer Chemotherapy

Research paper thumbnail of A New Approach for a Class of Optimal Control Problems of Volterra Integral Equations

Intelligent Control and Automation, 2011

In this paper, we propose a new approach for a class of optimal control problems governed by Volt... more 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.

Research paper thumbnail of Control of a class of nonsmooth dynamical systems

Journal of Vibration and Control, 2013

Research paper thumbnail of A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

Journal of Mathematics, 2013

We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth e... more 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.

Research paper thumbnail of A New Definition for Generalized First Derivative of Nonsmooth Functions

Applied Mathematics, 2011

In this paper, we define a functional optimization problem corresponding to smooth functions whic... more 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.

Research paper thumbnail of A numerical approach for nonsmooth ordinary differential equations

Journal of Vibration and Control, 2012

ABSTRACT In this paper, the authors proposed an approach for solving nonsmooth continuous and dis... more ABSTRACT In this paper, the authors proposed an approach for solving nonsmooth continuous and discontinuous ordinary differential equations which is based on a generalization of the Taylor expansion. First is considered a generalized derivative for nonsmooth functions with a single variable which is proposed by Kamyad et al. Then, the generalized Taylor expansion of nonsmooth functions is introduced and used to state an approach. Finally, some numerical examples of nonsmooth ordinary differential equations are solved.

Research paper thumbnail of Solving a Class of Non-Smooth Optimal Control Problems

In this paper, we first propose a new generalized derivative for non-smooth functions and then we... more In this paper, we first propose a new generalized derivative for non-smooth functions and then we utilize this generalized derivative to convert a class of non-smooth optimal control problem to the corresponding smooth form. In the next step, we apply the discretization method to approximate the obtained smooth problem to the nonlinear programming problem. Finally, by solving the last problem, we obtain an approximate optimal solution for main problem.