Academic Positions

  • 2013 Present

    Assistant Professor

    K. N. Toosi University of Tech, Faculty of Mathematical Science

Education & Training

  • Ph.D. 2012

    Ph.D. in Applied Mathematics & Optimization

    Sharif University of Tech

  • M.B.A.2007

    Master's Degree in Optimization

    Sharif University of Tech

  • B.A.2003

    Bachelor's Degree in Applied Mathematics

    University of Isfahan

Research Projects

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    My Ph.D. Thesis

    Design and analysis of filter trust-region algorithms for unconstrained and bound constrained optimization.

    A new filter-trust-region algorithm for solving unconstrained and bound constrained optimization problems is introduced. Based on the filter technique introduced by Fletcher and Leyffer, it extends the existing technique to the fully general unconstrained optimization problems. The new algorithm is equipped with a new filter technique guarantying the finiteness of the filter size. Moreover, the worst case complexity of the filter size is introduced. We have shown the method is globally convergent to at least one second-order critical point, and numerical experiments indicate that it is very competitive with more classical trust-region algorithms.

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    My Master Thesis

    Primal-Dual interior point algorithms for nonconvex optimization.

    Primal-dual interior methods for nonconvex nonlinear programming have recently been the subject of significant attention from the optimization community. Several different primal-dual methods have been suggested, along with some theoretical and numerical results. Although the underlying motivation for all of these methods is relatively uniform, there axe nonetheless substantive variations in crucial details, including the formulation of the nonlinear equations, the form of the associated linear system, the choice of linear algebraic procedures for solving this system, strategies for adjusting the barrier parameter and the Lagrange multiplier estimates, the merit function, and the treatment of indefiniteness. Not surprisingly, each of these choices can affect the theoretical properties and practical performance of the method. This thesis discusses the approaches to these issues that we took in implementing a specific primal-dual method.

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An efficient conjugate gradient method with strong convergence properties for non-smooth optimization

Fahimeh Abdollah,Masoud Fatemi
Journal Paper Journal of Mathematical Modeling, Volume , Issue , 2021, Pages

Abstract

In this paper, we introduce an efficient conjugate gradient method for solving nonsmooth optimization problems by using the Moreau-Yosida regularization approach. The search directions generated by our proposed procedure satisfy the sufficient descent property, and more importantly, belong to a suitable trust region. Our proposed method is globally convergent under mild assumptions. Our numerical comparative results on a collection of test problems show the efficiency and superiority of our proposed method. We have also examined the ability and the effectiveness of our approach for solving some real-world engineering problems from image processing field. The results confirm better performance of our method.

A new conjugate gradient method based on a modified secant condition with its applications in image processing

Fahimeh Abdollahi and Masoud Fatemi
Journal PaperRAIRO-Oper. Res. Volume 55, Issue 1, 2021, Page(s) 167-187

Abstract

We propose an effective conjugate gradient method belonging to the class of Dai–Liao methods for solving unconstrained optimization problems. We employ a variant of the modified secant condition and introduce a new conjugate gradient parameter by solving an optimization problem. The optimization problem combines the well-known features of the linear conjugate gradient method using some penalty functions. This new parameter takes advantage of function information as well as the gradient information to provide the iterations. Our proposed method is globally convergent under mild assumptions. We examine the ability of the method for solving some real-world problems from image processing field. Numerical results show that the proposed method is efficient in the sense of the PSNR test. We also compare our proposed method with some well-known existing algorithms using a collection of CUTEr problems to show its efficiency.

A new conjugate gradient method with an efficient memory structure.

Masoud Fatemi
Journal Paper Computational and Applied Mathematics, Volume 38, Issue 2, 2019, pages 1-17.

Abstract

A new family of conjugate gradient methods for large-scale unconstrained optimization problems is described. It is based on minimizing a penalty function, and uses a limited memory structure to exploit the useful information provided by the iterations. Our penalty function combines the good properties of the linear conjugate gradient method using some penalty parameters. We propose a suitable penalty parameter by solving an auxiliary linear optimization problem and show that the proposed parameter is promising. The global convergence of the new method is investigated under mild assumptions. Numerical results show that the new method is efficient and confirm the effectiveness of the memory structure.

A LIMITED MEMORY CLASS OF CONJUGATE GRADIENT METHODS

Masoud Fatemi
Journal Paper PACIFIC JOURNAL OF OPTIMIZATION, Volume 15, Issue 3, 2019, Pages 457-475

Abstract

We combine the good properties of the linear conjugate gradient algorithm using an optimization problem, and introduce a new limited memory class of nonlinear conjugate gradient methods. This new class contains Dai-Liao family as a subclass. Using this idea, we propose a bound for the optimal Dai-Liao parameter. The global convergence of the new method is investigated under mild assumptions. The numerical comparing results indicate that the new method is efficient and competitive with CG-DESCENT.

A scaled conjugate gradient method for nonlinear unconstrained optimization.

Masoud Fatemi
Journal Paper Optimization Methods and Software, Volume 32, Issue 5, 2017, Pages 1095-1112.

Abstract

We propose a new optimization problem which combines the good features of the classical conjugate gradient method using some penalty parameter, and then, solve it to introduce a new scaled conjugate gradient method for solving unconstrained problems. The method reduces to the classical conjugate gradient algorithm under common assumptions, and inherits its good properties. We prove the global convergence of the method using suitable conditions. Numerical results show that the new method is efficient and robust.

A new efficient conjugate gradient method for unconstrained optimization.

Masoud Fatemi
Journal Paper Journal of Computational and Applied Mathematics, Volume 300, 2016, Pages 207-216.

Abstract

We propose a nonlinear conjugate gradient method for unconstrained optimization based on solving a new optimization problem. Our optimization problem combines the good features of the linear conjugate gradient method using some penalty parameters. We show that the new method is a subclass of Dai–Liao family, the fact that enables us to analyze the family, closely. As a consequence, we obtain an optimal bound for Dai–Liao parameter. The global convergence of the new method is investigated under mild assumptions. Numerical results show that the new method is efficient and robust, and outperforms CG-DESCENT.

An optimal parameter for Dai–Liao family of conjugate gradient methods.

Masoud Fatemi
Journal Papers Journal of Optimization Theory and Applications, Volume 169, Issue 2, 2016, Pages 587-605

Abstract

We introduce a new efficient nonlinear conjugate gradient method for unconstrained optimization, based on minimizing a penalty function. Our penalty function combines the good properties of the linear conjugate gradient method using some penalty parameters. We show that the new method is a member of Dai–Liao family and, more importantly, propose an efficient Dai–Liao parameter by closely analyzing the penalty function. Numerical experiments show that the proposed parameter is promising.

Two extensions of the Dai-Liao method with sufficient descent property based on a penalization scheme.

Masoud Fatemi, S Babaie-Kafaki
Journal Paper Bull. Comput. Appl. Math, Volume 4, 2016, Pages 7-19.

Abstract

To achieve the good features of the linear conjugate gradient algorithm in a recent extension of the Dai-Liao method, two adaptive choices for parameter of the extended method are proposed based on a penalization approach. It is shown that the suggested parameters guarantee the sufficient descent property independent to the line search and the objective function convexity. Furthermore, they ensure the global convergence of the related algorithm for uniformly convex objective functions. Using a set of unconstrained optimization test problems from the CUTEr library, effectiveness of the suggested choices are numerically compared with two other recently proposed adaptive choices. Results of comparisons show that one of the proposed choices is computationally promising in the sense of the Dolan-Moré performance profile.

An interior-point method for P*(kappa)-linear complementarity problem based on a trigonometric kernel function.

S. Fathi Hafshejani,Masoud Fatemi, M. Reza Peyghami
Journal Paper Journal of Applied Mathematics and Computing, Volume 48, Issue 1, 2015, Pages 111-128

Abstract

Recently, El Ghami (Optim Theory Decis Mak Oper Res Appl 31:331–349, 2013) proposed a primal dual interior point method for -Linear Complementarity Problem (LCP) based on a trigonometric barrier term and obtained the worst case iteration complexity as for large-update methods. In this paper, we present a large update primal–dual interior point algorithm for -LCP based on a new trigonometric kernel function. By a simple analysis, we show that our algorithm based on the new kernel function enjoys the worst case iteration bound for solving -LCP. This result improves the worst case iteration bound obtained by El Ghami for -LCP based on trigonometric kernel functions significantly.

A PROJECTED GRADIENT FILTER TRUST-REGION ALGORITHM FOR BOUND CONSTRAINED OPTIMIZATION.

Masoud Fatemi, N. Mahdavi-Amiri
Journal PaperPACIFIC JOURNAL OF OPTIMIZATION, Volume 10, Issue 1, 2014, Pages 229-242

Article

We present a filter trust-region algorithm for solving bound constrained optimization problems. The algorithm is an extension of our method recently proposed for unconstrained optimization to consider the bound constraints. The new algorithm combines the gradient projection method with the filter technique to generate non-monotone iterations. In contrast with the earlier filter algorithms, the new algorithm has the novelty to ensure the finiteness of the filter size. Global convergence to at least one first order critical point is established. Comparative numerical results on a set of test problems from the CUTEr collection show the algorithm is competitive and more efficient solely with respect to the filter size.

A modified two-point stepsize gradient algorithm for unconstrained minimization.

Saman Babaie-Kafaki, Masoud Fatemi
Journal Paper Optimization Methods and Software, Volume 28, Issue 5, 2013, Pages 1040-1050

Abstract

Based on a modified secant equation proposed by Li and Fukushima, we derive a stepsize for the Barzilai–Borwein gradient method. Then, using the newly proposed stepsize and another effective stepsize proposed by Dai et al. in an adaptive scheme that is based on the objective function convexity, we suggest a modified two-point stepsize gradient algorithm. We also show that the limit point of the sequence generated by our algorithm is first-order critical. Finally, our numerical comparisons done on a set of unconstrained optimization test problems from the CUTEr collection are presented. At first, we compare the performance of our algorithm with two other two-point stepsize gradient algorithms proposed by Dai et al. and Raydan. Then, numerical comparisons between the implementations of our algorithm and two conjugate gradient methods proposed by Gilbert and Nocedal, and Hestenes and Stiefel, and also...

A non-monotone trust region algorithm for unconstrained optimization with dynamic reference iteration updates using filter

Masoud Fatemi, Nezam Mahdavi-Amiri
Journal Papers Optimization, Volume 61, Issue 6, 2012, Pages 733-763

Abstract

We present a non-monotone trust region algorithm for unconstrained optimization. Using the filter technique of Fletcher and Leyffer, we introduce a new filter acceptance criterion and use it to define reference iterations dynamically. In contrast with the early filter criteria, the new criterion ensures that the size of the filter is finite. We also show a correlation between problem dimension and the filter size. We prove the global convergence of the proposed algorithm to first- and second-order critical points under suitable assumptions. It is significant that the global convergence analysis does not require the common assumption of monotonicity of the sequence of objective function values in reference iterations, as assumed by the standard non-monotone trust region algorithms. Numerical experiments on the CUTEr problems indicate that the new algorithm is competitive compared to some representative non-monotone trust.

A filter trust-region algorithm for unconstrained optimization with strong global convergence properties

Masoud Fatemi, N Mahdavi-Amiri
Journal Paper Computational Optimization and Applications, Volume 52, Issue 1, 2012, Pages 239-266

Abstract

We present a new filter trust-region approach for solving unconstrained nonlinear optimization problems making use of the filter technique introduced by Fletcher and Leyffer to generate non-monotone iterations. We also use the concept of a multidimensional filter used by Gould et al. (SIAM J. Optim. 15(1):17–38, 2004) and introduce a new filter criterion showing good properties. Moreover, we introduce a new technique for reducing the size of the filter. For the algorithm, we present two different convergence analyses. First, we show that at least one of the limit points of the sequence of the iterates is first-order critical. Second, we prove the stronger property that all the limit points are first-order critical for a modified version of our algorithm. We also show that, under suitable conditions, all the limit points are second-order critical. Finally, we compare our algorithm with a natural trust-region algorithm and the ..

Two effective hybrid conjugate gradient algorithms based on modified BFGS updates

Saman Babaie-Kafaki,Masoud Fatemi, Nezam Mahdavi-Amiri
Journal Paper Numerical Algorithms, Volume 58, Issue 3, 2011, Pages 315-331

Abstract

Based on two modified secant equations proposed by Yuan, and Li and Fukushima, we extend the approach proposed by Andrei, and introduce two hybrid conjugate gradient methods for unconstrained optimization problems. Our methods are hybridizations of Hestenes-Stiefel and Dai-Yuan conjugate gradient methods. Under proper conditions, we show that one of the proposed algorithms is globally convergent for uniformly convex functions and the other is globally convergent for general functions. To enhance the performance of the line search procedure, we propose a new approach for computing the initial value of the steplength for initiating the line search procedure. We give a comparison of the implementations of our algorithms with two efficiently representative hybrid conjugate gradient methods proposed by Andrei using unconstrained optimization test problems from the CUTEr collection.

A Modified Conjugate Gradient Method for Nonsmooth Optimization Problems

Fahimeh Abdollahi, Masoud Fatemi
Conference Papers 51 Annual Mathematic Conference, 2021.

A New Conjugate Gradient Method for Unconstrained Optimization

Fahimeh Abdollahi, Masoud Fatemi
Conference Papers The 12th International Conference of Iranian Operations Research Society, 2019.

A filter Barzilai-Borwein method

F. Arzani, Masoud Fatemi, M. Peyghami
Conference Papers The 7th International Conference of Iranian Operations Research Society, 2014.

A globally convergent trust-region algorithm for unconstrained optimization using filter

Masoud Fatemi, M. Mahdavi-Amiri
Conference Papers The 4th International Conference of Iranian Operations Research Society, 2011.

Currrent Teaching

  • Present 2021

    Network Optimization

    The purpose of this course is to examine in detail various strategies for solving network optimization problems such as Minimum cost flow problem, Shortest path problem, Maximum flow problem and so on.

  • Present 2021

    Advanced Non-linear Optimization

    The purpose of this course is to examine in detail various strategies for solving mathematical optimization problems from unconstrained to constrained.

Teaching History

  • 2020 2018

    Advanced Linear Optimization

    The purpose of this Course is to examine in detail various strategies for solving linear programming problems and for extending the linear programming results to more general classes of mathematical programming problems.

  • 2020 2018

    Linear Optimization

    A linear program is an optimization problem that seeks to minimize or maximize a linear function subject to a system of linear inequality and/or equality constraints. Applications of linear programs include transportation problems, flight scheduling, corporate planning, linear and nonlinear curve fitting, product mix, load balancing, production scheduling, inventory control, and many others. This course will cover the simplex method in detail, emphasizing both mathematical foundations as well as computational considerations for effective computer implementations.

  • 2020 ----

    Numerical Methods for Data Science

    This is a survey course on numerical methods prominent in modern data analysis and machine learning. Building on basic methods of optimization and numerical linear algebra, the course will explore the role of numerical methods for treating several classes of data analysis problems, including low rank factorizations and completion of matrix data; function approximation by kernel methods; and analysis of data on graphs.

At My Office

You can find me at my office located at mathematic department of K. N. Toosi University of Technology.

I am at my office every day from 9:00 Am until 4:00 Pm, but you may consider sending an email or calling me to fix an appointment.

  K.N.Toosi University of Technology Faculty of Mathematics Daneshgah Boulevard, Ehsan Street Exit, East Zeynoddin Highway, Tehran, Iran