Papers by Maryam Zangiabadi
International Conference on Systems, Jul 11, 2005
In the real-world optimization problems, coefficients of the objective function are not known pre... more In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters (FLP). Then by using the concept of comparison of fuzzy numbers we transform FLP problem into a multiobjective linear programming (MOLP) problem. To this end, we propose several theorems which are used to obtain optimal solutions of FLP. Finally an example is given to illustrate the proposed method of solving linear programming problem with fuzzy parameters (FLP).
An arc search interior-point algorithm for monotone symmetric cone linear complementarity problem... more An arc search interior-point algorithm for monotone symmetric cone linear complementarity problem is presented. The algorithm estimates the central path by an ellipse and follows an ellipsoidal approximation of the central path to reach an ε-approximate solution of the problem in a wide neighborhood of the central path. The convergence analysis of the algorithm is derived. Furthermore, we prove that the algorithm has the complexity bound O (√ rL) using Nesterov-Todd search direction and O (rL) by the xs and sx search directions. The obtained iteration complexities coincide with the best-known ones obtained by any proposed interiorpoint algorithm for this class of mathematical problems.
Bulletin of The Iranian Mathematical Society, Jun 1, 2011
In [H. Mansouri and C. Roos, Numer. Algorithms 52 (2009) 225-255.], Mansouri and Ross presented a... more In [H. Mansouri and C. Roos, Numer. Algorithms 52 (2009) 225-255.], Mansouri and Ross presented a primal-dual infeasible interior-point algorithm with full-Newton steps whose iteration bound coincides with the best known bound for infeasible interior-point methods. Here, we introduce a slightly different algorithm with a different search direction and show that the same complexity result is obtained using a simpler analysis.
Optimization, Sep 25, 2016
In this paper, we propose a predictor-corrector infeasible interior-point algorithm for semidefin... more In this paper, we propose a predictor-corrector infeasible interior-point algorithm for semidefinite optimization based on the Nesterov-Todd scaling scheme. In each iteration, the algorithm computes the new iterate using a new combination of the predictor and corrector directions. Using the Ai-Zhang's wide neighborhood for linear complementarity problems, and extended to semidefinite optimization by Li and Terlaky, it is shown that the iteration complexity bound of the algorithm is O(n 5 4 log ε −1), where n is the dimension of the problem and ε is the required precision.
Journal of New Researches in Mathematics, Feb 1, 2016
In this paper, we propose a feasible interior-point algorithm for mixed symmetric cone linear com... more In this paper, we propose a feasible interior-point algorithm for mixed symmetric cone linear complementarity problems which are a general class of complementarity problems. The symmetrization of the search directions used in this paper is based on Nesterov and Todd scaling scheme. By using Euclidean Jordan algebra, we prove the convergence analysis of the proposed algorithm and show that the complexity bound of the algorithm matches the currently best known iteration bound for feasible interior-point methods.
In today's highly competitive market, the pressure on organizations to find a better way to creat... more In today's highly competitive market, the pressure on organizations to find a better way to create and deliver value to customers is mounting. The decision involves many quantitative and qualitative factors that may be conflicting in nature. Here, we present a new model for transportation problem with consideration of quantitative and qualitative data. In the model, we quantify the qualitative data by using the weight assessment technique in the fuzzy analytic hierarchy process. Then, a preemptive fuzzy goal programming model is formulated to solve the proposed model. The software package LINGO is used for solving the fuzzy goal programming model. Finally, a numerical example is given to illustrate that the proposed model may lead to a more appropriate solution.
Asia-Pacific Journal of Operational Research, Aug 1, 2007
In the real-world optimization problems, coefficients of the objective function are not known pre... more In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters (FLP). Then by using the concept of comparison of fuzzy numbers we transform FLP problem into a multiobjective linear programming (MOLP) problem. To this end, we propose several theorems which are used to obtain optimal solutions of FLP. Finally an example is given to illustrate the proposed method of solving linear programming problem with fuzzy parameters (FLP).
A full-Newton step infeasible-interior-point algorithm for linear complementarity problems
Nonlinear Analysis-real World Applications, Feb 1, 2011
ABSTRACT This paper consists of two parts. In the first part we present a new primal-dual feasibl... more ABSTRACT This paper consists of two parts. In the first part we present a new primal-dual feasible interior-point algorithm for solving monotone linear complementarity problems (LCP). Since the algorithm uses only full-Newton steps, it has the advantage that no line-searches are needed. It is proven that the number of iterations of the algorithm is , which coincides with the well-known best iteration bound for LCP. In the second part, we generalize an infeasible interior-point method for linear optimization introduced by Roos (2006) [15] to LCP. Two types of full-Newton steps are used, feasibility steps and (ordinary) centering steps, respectively. The algorithm starts from strictly feasible iterates of a perturbed problem, on its central path, and feasibility steps find strictly feasible iterates for the next perturbed problem. By using centering steps for the new perturbed problem, we obtain strictly feasible iterates close enough to the central path of the new perturbed problem. The starting point depends on two positive numbers ρp and ρd. The algorithm terminates either by finding an ε-solution or detecting that the LCP problem has no optimal solution with vanishing duality gap satisfying a condition in terms of ρp and ρd. The iteration bound coincides with the currently best iteration bound for linear complementarity problems.
Full Nesterov–Todd step infeasible interior-point method for symmetric optimization
European Journal of Operational Research, Nov 1, 2011
ABSTRACT Euclidean Jordan algebras were proved more than a decade ago to be an indispensable tool... more ABSTRACT Euclidean Jordan algebras were proved more than a decade ago to be an indispensable tool in the unified study of interior-point methods. By using it, we generalize the full-Newton step infeasible interior-point method for linear optimization of Roos [Roos, C., 2006. A full-Newton step O(n) infeasible interior-point algorithm for linear optimization. SIAM Journal on Optimization. 16 (4), 1110–1136 (electronic)] to symmetric optimization. This unifies the analysis for linear, second-order cone and semidefinite optimizations.
Developing the Optimal Model for Correct Use of Environmental Resources in Chelgerd Watershed
ENVIRONMENTAL SCIENCES, 2018
How much is enough? Government subsidies in supporting green product development
European Journal of Operational Research, Sep 1, 2023
A New Wide Neighborhood Primal-Dual Predictor-Corrector Interior-Point Method for Linear Programming
Numerical Functional Analysis and Optimization, 2016
ABSTRACT In this article, we present a new predictor-corrector interior-point method, based on a ... more ABSTRACT In this article, we present a new predictor-corrector interior-point method, based on a wide neighborhood of the central path, for linear programming problems. In the corrector step ofthe proposed method, we derive the step size and corrector directions that guarantee that each iteration lies in a wide neighborhood of the central path. We also prove that the algorithm has iteration complexity, which coincides with the best bound derived for linear programming problems.
Operations Research Letters, 1994
We present a predictor ~corrector algorithm for solving a primal dual pair of linear programming ... more We present a predictor ~corrector algorithm for solving a primal dual pair of linear programming problems, The algorithm starts from an infeasible interior point and it solves the pair in O(nL) iterations, where n is the number of variables and L is the size of the problems. At each iteration of the algorithm, the predictor step decreases the infeasibility and the corrector step decreases the duality gap. The main feature of the algorithm is the simplicity of the predictor step, which performs a line search along a fixed search direction computed at the beginning of the algorithm. The corrector step uses a procedure employed in a feasible-interior-point algorithm. The proof of polynomiality is also sirnple.
Efficiency Evaluation of LP-MOLA, FLP-MOLA and GP-MOLA Mathematical-Spatial Optimization Models in Environmental Planning
Corresponding author. Tel.:+989131850756 E-mail address: [email protected] Article info Ab... more Corresponding author. Tel.:+989131850756 E-mail address: [email protected] Article info Abstract Article history: Received 06 Novemver 2016 Accepted 06 December 2016 Available online 1 Junuary 2017 In recent years, due to absence of integrated watershed management in most regions, natural resources have witnessed numerous damages with severe floods as one of its consequences which further leads to economic, social and environmental damages. Presently, there is no optimal utilization of land in most watersheds hence no optimal model matching with facilities and objectives is used in the watersheds. Thus, management and planning are essential for the proper utilization, protection and revival of these resources. This study aims to develop some mathematical-spatial optimum utilization environmental plans in watershed using LP, FLP and GP mathematical optimization approaches including environmental and economic objectives while considering social issues. About the LP model the re...
The Effects of Government Subsidies on the Development of Green Products
This thesis tackles the problem of a monopolist firm that is considering designing products with ... more This thesis tackles the problem of a monopolist firm that is considering designing products with environmental qualities while facing significant research and development costs. A mathematical formulation is adopted to model the impact of government subsidies on the firm's choice between mass marketing, where only one standard product serves the entire market, and market segmentation, in which the firm develops ordinary and green products for two market segments. The firm's behavior in reaction to the subsidies is analyzed through a two-stage Stackelberg game. The obtained results reveal that the subsidy level does not affect the relationships between the environmental qualities of the manufactured products under different marketing strategies when the green market is not strong. Our analyses also demonstrate how an optimal subsidy level should be selected to maximize the social welfare, and how this optimal subsidy is impacted by various parameters such as the magnitude of ...
We present an infeasible interior-point predictor-corrector algorithm, based on a large neighborh... more We present an infeasible interior-point predictor-corrector algorithm, based on a large neighborhood of the central path, for the general Phorizontal linear complementarity problem over the Cartesian product of symmetric cones. The polynomial convergence is shown for the commutative class of search directions. We specialize our algorithm further by prescribing some scaling elements and also consider the case of feasible starting points. We believe this to be the first interior-point method based on large neighborhoods for the P-horizontal linear complementarity problems over the Cartesian product of symmetric cones.
Bulletin of The Iranian Mathematical Society, 2016
In this paper, we propose a feasible interior-point method for convex quadratic programming ... more In this paper, we propose a feasible interior-point method for convex quadratic programming over symmetric cones. The proposed algorithm relaxes the accuracy requirements in the solution of the Newton equation system, by using an inexact Newton direction. Furthermore, we obtain an acceptable level of error in the inexact algorithm on convex quadratic symmetric cone programming (CQSCP). We also prove that the iteration bound for the feasible short-step method is $O(sqrt{n}logfrac{1}{varepsilon})$, and $O(nlogfrac{1}{varepsilon})$ for the large-step method which coincide with the currently best known iteration bounds for CQSCPs.
Iranian Journal of Fuzzy Systems, 2013
The linear multiobjective transportation problem is a special type of vector minimum problem in w... more The linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conicting in nature. This paper presents an application of fuzzy goal programming to the linear multiobjective transportation problem. In this paper, we use a special type of nonlinear (hyperbolic and exponential) membership functions to solve multiobjective transportation problem. It gives an optimal compromise solution. The obtained result has been compared with the solution obtained by using a linear membership function. To illustrate the methodology some numerical examples are presented.
Many efficient interior-point methods (IPMs) are based on the use of a self-concordant barrier fu... more Many efficient interior-point methods (IPMs) are based on the use of a self-concordant barrier function for the domain of the problem that has to be solved. Recently, a wide class of new barrier functions has been introduced in which the functions are not self-concordant, but despite this fact give rise to efficient IPMs. Here, we introduce the notion of locally self-concordant barrier functions and we prove that the new barrier functions are locally self-concordant. In many cases, the (local) complexity numbers of the new barrier functions along the central path are better than the complexity number of the logarithmic barrier function by a factor between 0.5 and 1.
A weighted-path following interior-point algorithm for Cartesian $P_*(\kappa)$-LCP over symmetric cones
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Papers by Maryam Zangiabadi