مازیار صلاحی
دانشگاه گیلان، دانشکده علوم ریاضی
[ 1 ] - شفاف سازی تصاویر با استفاده از تجزیه مقادیر تکین و الگوریتم های بهینه سازی
شفاف سازی تصاویر یکی از مسائل مهم پردازش تصویر به شمار می رود و از نوع مسائل وارون است. روشهای کلاسیک برای حل این نوع مسائل روشهای گسسته سازی هستند که به دلیل بدحالت بودن ماتریس ضرایب معمولا به جواب قابل قبول منجر نمی شوند. در اینجا ابتدا به معرفی مقدمات مورد نیاز جبرخطی در پردازش تصویر می پردازیم و سپس مفاهیم اولیه تصویر را بیان می کنیم. در ادامه رفتار روشهای منظم سازی، تجزیه مقادیر تکین و ...
[ 2 ] - Robust portfolio selection with polyhedral ambiguous inputs
Ambiguity in the inputs of the models is typical especially in portfolio selection problem where the true distribution of random variables is usually unknown. Here we use robust optimization approach to address the ambiguity in conditional-value-at-risk minimization model. We obtain explicit models of the robust conditional-value-at-risk minimization for polyhedral and correlated polyhedral am...
[ 3 ] - SDO relaxation approach to fractional quadratic minimization with one quadratic constraint
In this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. First we introduce a parametric equivalent of the problem. Then a bisection and a generalized Newton-based method algorithms are presented to solve it. In order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...
[ 4 ] - آشنایی با برنامه ریزی روی مخروط های درجه دوم
در این مقاله، با توجه به کاربردهای روزافزون مسائل برنامه ریزی روی مخروط ها از جمله مخروطهای درجه دوم، به معرفی این مسائل می پردازیم. ابتدا مفاهیم پایه ای مربوط به این زمینه را بیان کرده سپس به معرفی دوگان یک مساله برنامه ریزی خطی روی مخروط درجه دوم می پردازیم. در ادامه به معرفی جبر جردن روی مخروط های درجه دوم می پردازیم و با استفاده از آن، شرایط بهینگی را برای مسائل مذکور بیان و اثبات می کنیم.
[ 5 ] - A Semidefinite Optimization Approach to Quadratic Fractional Optimization with a Strictly Convex Quadratic Constraint
In this paper we consider a fractional optimization problem that minimizes the ratio of two quadratic functions subject to a strictly convex quadratic constraint. First using the extension of Charnes-Cooper transformation, an equivalent homogenized quadratic reformulation of the problem is given. Then we show that under certain assumptions, it can be solved to global optimality using semidefini...
[ 6 ] - بررسی فلوریستیک، کورولوژی و مدل توزیع فراوانی گیاهان پارک جنگلی بی بی یانلو آستارا
The aim of this study was to investigate vegetation composition in broadleaved and conifers plantations in 220 ha of Loblloly pine (Pinus taeda), alder (Alnus glutinosa( and poplar (Popolus deltoides) hardwood plantations and its comparison with natural forests in Bibiyanlu protected forest park, Astara. A total of 60 sampling plots of 1000 m2 were taken using randomly-systematic method with1...
[ 7 ] - مدل میانگین انحراف مطلق با عدم قطعیت روی بازده‌ها برای بهینه سازی سبد سهام
In this paper, mean absolute deviation model for optimal portfolio selection problem is studied. Due to the uncertainty in the observed returns from financial markets, an improved robust formulation based on Bertsimas and Sim approach is presented. Then we study the robust model of the problem under correlated uncertainty set and give its equivalent model. Finally, the performance of the imp...
[ 8 ] - یک الگوریتم کارا برای زیر مساله‌ی ناحیه اطمینان توسیع یافته با دو قید خطی
Trust region subproblem (TRS), which is the problem of minimizing a quadratic function over a ball, plays a key role in solving unconstrained nonlinear optimization problems. Though TRS is not necessarily convex, there are efficient algorithms to solve it, particularly in large scale. Recently, extensions of TRS with extra linear constraints have received attention of several researchers. It ha...
[ 9 ] - On SOCP/SDP Formulation of the Extended Trust Region Subproblem
We consider the extended trust region subproblem (eTRS) as the minimization of an indefinite quadratic function subject to the intersection of unit ball with a single linear inequality constraint. Using a variation of the S-Lemma, we derive the necessary and sufficient optimality conditions for eTRS. Then, an OCP/SDP formulation is introduced for the problem. Finally, several illustrative examp...
[ 10 ] - Additive slacks- based measure with undesirable output and feedback for a two-stage structure
This paper develops slacks-based measure (SBM) and additive SBM (ASBM) to evaluate efficiency of decision making units (DMUs) in a two-stage structure with undesirable outputs and feedback variables from the internal perspective. The SBM model is linearized for a specific weight and the ASBM model is reformulated as a second order cone program. The target values for all inputs, outputs (both d...
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