Jun 1, 2010 - 7 Subgradient method for constrained optimization. 21 ... extremely large problems for which interior-poin
Jun 1, 2010 - The step lengths are not chosen via a line search, as in the ordinary gradient method. In the most ... con
Jun 8, 2018 - f and g are subdifferentiable. This means Assumption 3.2 (II) guarantees that âf(x) ̸= â and âg(y) ̸= â for every x â H1 and y â H2.
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step lengths that are fixed ahead of time, instead of an exact or approximate line search as ..... the constrained convex optimization problem minimize f(x).
METHOD FOR DC PROGRAMMING AND ITS APPLICATIONS. Jian Gu ... ous differentiable, f1, f2 are convex and g, h are lower semicontinuous convex.
Oct 27, 2014 - function Ï = Iuâ¤b can be interpreted as imposing a total budget given by b ... In light of this fact, much attention has been dedicated to the random .... The server has to make an irrevocable decision by choosing xt â {0, 1}.
For a convex function c : H â R, c is said to be subdifferentiable at a point x â H ... We say c is subdifferentiable on H, if c is subdifferentiable at each x â H. It is ...
AbstractâWe consider constrained minimization of a sum of convex functions over a convex and compact set, when each component function is known only to a ...
THE demand for large-scale networks consisting of multi- ple agents (i.e., nodes) with ... distributed data mining scenario, privacy considerations may ... [email protected]). M. O. Sayin ... a deterministic analysis of the SGD iterates and our results bui
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Y. Censor. Department of Mathematics, University of Haifa, Mt. Carmel, 31905 Haifa, Israel. A. Gibali. Department of ... [email protected] . Communicated by ...
subgradient estimate and then the Liouville-type theorem for the CR heat ... parabolic Li-Yau gradient estimate and Li-Yau Harnack inequality for the positive.
Lagrangean relaxation is a well known relaxation technique frequently used to give bound information to combinatorial optimization problems [see for example ...
AbstractâPrices in electricity markets are given by the dual variables ... unit commitment and economic dispatch problem, except that the costs in this ...... [15] D. Kirschen, G. Strbac, and J. Wiley, Fundamentals of power system economics.
The methods presented by Herron 9] and Nielson 11] fall into this latter category. The tters for these non-B ..... 1] Bruce G. Baumgart. Geometric modeling for ...
In [17], the author assumed that f is convex and subdifferentiable on H with respect to ... Therefore, the assumption of subdifferentiability is indeed not necessary.
D.1 [Software]: Programming Techniques. General ..... provides convenient syntactic support for monadic programming. ... fun modl f = mod (fn (NIL,NIL) => true.
Department of Computer Science, University of Wales, Cardiff, PO Box 916, .... tion 4 show that our method is consistently the best for classifying, yet loses.
Apr 22, 2007 - Dan Butnariu1, Yair Censor1, Pini Gurfil2 and Ethan Hadar3. 1Department .... the CFP was given by Censor and Lent [19] as follows. Algorithm ...
Feb 28, 2011 - +â] is convex and subdifferentiable at x, for all x â C (see [8, 13, 15, 18]). In [8] the subdifferential of this function is called diagonal ...
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Incremental gradient methods for differentiable unconstrained problems have a long tra- dition ...... M., Stochastic Programming Methods, Nauka, Moscow, 1976.
Sept. 1999, Revised Feb., 2001
LIDS-P-2460
To Appear in SIAM J. on Optimization
INCREMENTAL SUBGRADIENT METHODS1 FOR NONDIFFERENTIABLE OPTIMIZATION by Angelia Nedi´ c and Dimitri P. Bertsekas
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Abstract We consider a class of subgradient methods for minimizing a convex function that consists of the sum of a large number of component functions. This type of minimization arises in a dual context from Lagrangian relaxation of the coupling constraints of large scale separable problems. The idea is to perform the subgradient iteration incrementally, by sequentially taking steps along the subgradients of the component functions, with intermediate adjustment of the variables after processing each component function. This incremental approach has been very successful in solving large differentiable least squares problems, such as those arising in the training of neural networks, and it has resulted in a much better practical rate of convergence than the steepest descent method. In this paper, we establish the convergence properties of a number of variants of incremental subgradient methods, including some that are stochastic. Based on the analysis and computational experiments, the methods appear very promising and effective for important classes of large problems. A particularly interesting discovery is that by randomizing the order of selection of component functions for iteration, the convergence rate is substantially improved.
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Research supported by NSF under Grant ACI-9873339. Dept. of Electrical Engineering and Computer Science, M.I.T., Cambridge, Mass., 02139. 1
1. Introduction 1. INTRODUCTION Throughout this paper, we focus on the problem minimize
