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Register a new userThe use of semi-stochastic gradient methods to solve some issues stochastic non-convex and non-smooth optimization
استخدام الطرائق العشوائيَّة شبه المتدرجة لحل بعض مسائل الأمثليات العشوائيَّة غير المحدّبة وغير الملساء.
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مبارك ديب( باحث )
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الغاية من البحث هي دراسة وتحليل بعض الطرائق العشوائيَّة شبه المتدرّجة وإمكانية تطبيقها لإيجاد الحل الأمثل لمسائل أمثليّة تخضع لمؤثّرات عشوائيّة وظروف تتحكّم فيها الصدفة. وقد تم إثبات تقارب بعض هذه الطرق الرياضيّة وفعاليتها من أجل بعض المسائل العشوائيَّة غير المحدّبة وغير الملساء والمزوّدة بدالة هدفية وقيود محدّدة وحيث اتخذ مجمّع الطاقة الشمسية كمثال على ذلك.
The purpose of research is the study and analysis of some of the stochastic semi-gradient methods and their applicability to find the optimal solution for the issues of optimization are subject to the effects Random and conditions are controlled by chance, as we proved the convergence of some of these mathematical methods and their effectiveness for some of the issues of stochastic non-convex and equipped objective function and specific constraints and where taken energy complex solar as an example
References used
MIHALEVECHV.C.GUPALA.M.NORKIN V.I. non convex optimization techniques- m. Science 1997. 280S
YRMOLIEV. U.M. YASTREMCKI. A.E. Methods of stochastic programming problems of Planning reserves- cybernetics ,1999, 320 c
NIKIFOROVV.A. mathematical simple model of solar collector heating buildings- heliotekhnika.1983. №1,pp56-80
KUTLEEVK.K.,SEYITKURBANOV C.SEKAEV V. A. , URYASEVS.P. calculation method of autonomous systems water and electricity to the helio-wind power plants. Ashgabat. NGOs*Sun*Turkmenian Academy of Sciences, 1987 35C
FOUSKAKIS, D. and DRAPER,D. Stochastic Optimization:2002
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The purpose of this research is to study and create a mathematical model under the terms of the probability of randomly imposed, specially by building a model of random Complex Solar particular by removing the salinity of the water, and thus to obtai
n fresh water and that, under certain conditions.
We Assure that the question of finding the optimum values for the variables solar collector above represent varieties of special issues of mathematical modeling and nonlinear stochastic, we point to that the most effective ways to find the perfect solution for this kind of issues are stochastic gradient methods
Conjugate gradient algorithms are important for solving unconstrained optimization
problems, so that we present in this paper conjugate gradient algorithm depending on
improving conjugate coefficient achieving sufficient descent condition and globa
l
convergence by doing hybrid between the two conjugate coefficients [1] and
[2]. Numerical results show the efficiency of the suggested algorithm after its
application on several standard problems and comparing it with other conjugate gradient
algorithms according to number of iterations, function value and norm of gradient vector.
Interior point methods are considered the most powerful tools for solving
linear, quadratic and nonlinear programming. In each iteration of interior
point method (IPM) at least one linear system has to be solved. The main
computational effort of I
PMs consist in the computational of these linear
systems. That drives many researchers to tackle this subject, which make this
area of research very active. The issue of finding a preconditioner for this
linear system was investigated in many papers.
In this paper, we provide a preconditioner for interior point methods for
quadratic programming. This preconditioner makes the system easier to be
solved comparing with the direct approach.
The preconditioner used follows the ideas, which is used for linear
approach. An explicit null space representation of linear constraints is
constructed by using a non-singular basis matrix identified from an estimate of
the optimal partition. This is achieved by means of efficient basis matrix
factorisation techniques used in implementations of the revised simplex
method.
This work deals with a new method for solving Integer Linear Programming Problems depending on a previous methods for solving these problems, such that Branch and Bound method and Cutting Planes method where this new method is a combination between t
hem and we called it Cut and Branch method. The reasons which led to this combination between Cutting Planes method and Branch and Bound method are to defeat from the drawbacks of both methods and especially the big number of iterations and the long time for the solving and getting of a results between the results of these methods where the Cut and Branch method took the good properties from the both methods. And this work deals with solving a one problem of Integer Linear Programming Problems by Branch and Bound method and Cutting Planes method and the new method, and we made a programs on the computer for solving ten problems of Integer Linear Programming Problems by these methods then we got a good results and by that, the new method (Cut and Branch) became a good method for solving Integer Linear Programming Problems. The combination method which we doing in this research opened a big and wide field in solving Integer Linear Programming Problems and finding the best solutions for them where we did the combination method again between the new method (Cut and Branch) and the Cutting Planes method then we got a new method with a very good results and solutions.
Defining some of the essential definitions and conceptions.
Stochastic matrix.
Stability.
Approximate stability.
Approximate stability in the quadratic middle.
Formula of a system of unsettled non stationary stochastic
differential equations.
Formula of a generalized system of unsettled non- stationary
stochastic differential equations.
Foundations of a system of differential equations that divines the
partial moments of the second order.
Foundations of a system of differential equations that divines
matrices of Lyapunov's functions.
The necessary and sufficient conditions formatrisses of Lyapunov's
functions to assure the stability of the studied system's solution
approximately in the quadratic middle.
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