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Titlebook: Lectures on Convex Optimization; Yurii Nesterov Textbook 2018Latest edition Springer Nature Switzerland AG 2018 complexity.complexity theo

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Polynomial-Time Interior-Point Methods of a self-concordant function. It appears that such a function can be easily minimized by the Newton’s Method. On the other hand, an important subclass of these functions, the self-concordant barriers, can be used in the framework of path-following schemes. Moreover, it can be proved that we can fo
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The Primal-Dual Model of an Objective Functionones. However, very often we know the explicit structure of the functional components. In this chapter we show how this knowledge can be used to accelerate the minimization methods and to extract a useful information about the dual counterpart of the problem. The main acceleration idea is based on t
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Optimization in Relative Scale corresponding inequality contains unknown parameters (Lipschitz constant, distance to the optimum). However, in many cases the required level of relative accuracy is quite understandable. To develop methods which compute solutions with relative accuracy, we need to employ internal structure of the
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Yurii Nesterovs, has been hampered by several biological characteristics of these mic- organisms: they cannot be grown in the absence of a plant host and their genetic structure is very complex. Despite these limitations, biologists have made important progress in understanding better the functioning of AM fungi.
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Yurii Nesterovs, has been hampered by several biological characteristics of these mic- organisms: they cannot be grown in the absence of a plant host and their genetic structure is very complex. Despite these limitations, biologists have made important progress in understanding better the functioning of AM fungi.
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Optimization in Relative Scaleubgradient method, which computes an approximate maximum of a positive convex function with certain relative accuracy. We show how to apply this method to solve problems of fractional covering, maximal concurrent flow, semidefinite relaxation, online optimization, portfolio management, and others. F
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