Results 11  20
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72
Executive Summary
 Usability Inspection Methods
, 1994
"... The fact that membrane proteins are notoriously difficult to analyse using standard protocols for atomicresolution structure determination methods have motivated adaptation of these techniques to membrane protein studies as well as development of new technologies. With this motivation, liquidstate ..."
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The fact that membrane proteins are notoriously difficult to analyse using standard protocols for atomicresolution structure determination methods have motivated adaptation of these techniques to membrane protein studies as well as development of new technologies. With this motivation, liquidstate nuclear magnetic resonance (NMR) has recently been used with success for studies of peptides and membrane proteins in detergent micelles, and solidstate NMR has undergone a tremendous evolution towards characterization of membrane proteins in native membrane and oriented phospholipid bilayers. In this minireview, we describe some of the technological challenges behind these efforts and provide examples on their use in membrane biology.
DUAL COORDINATE STEP METHODS FOR LINEAR NETWORK FLOW PROBLEMS
, 1988
"... We review a class of recentlyproposed linearcost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of ecomplementary slackness, and most do not explicitly manipulate any "global " objects such as paths, trees, or cuts. Int ..."
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Cited by 31 (8 self)
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We review a class of recentlyproposed linearcost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of ecomplementary slackness, and most do not explicitly manipulate any "global " objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of new serial computational complexity results. We develop the basic theory of these methods and present two specific methods, the erelaxation algorithm for the minimumcost flow problem, and the auction algorithm for the assignment problem. We show how to implement these methods with serial complexities of O(N 3 log NC) and O(NA log NC), respectively. We also discuss practical implementation issues and computational experience to date. Finally, we show how to implement erelaxation in a completely asynchronous, "chaotic" environment in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays.
Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces
 COMM. CONTEMP. MATH
, 2001
"... The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions are extended from Euclidean to Banach spaces. A pertinent duality theory is developed and several useful characterizations are given. The proofs rely on new results on the more subtle beh ..."
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Cited by 30 (15 self)
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The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions are extended from Euclidean to Banach spaces. A pertinent duality theory is developed and several useful characterizations are given. The proofs rely on new results on the more subtle behavior of subdifferentials and directional derivatives at boundary points of the domain. In weak Asplund spaces, a new formula allows the recovery of the subdifferential from nearby gradients. Finally, it is shown that every Legendre function on a reflexive Banach space is zone consistent, a fundamental property in the analysis of optimization algorithms based on Bregman distances. Numerous illustrating examples are provided.
Randomized Online PCA Algorithms with Regret Bounds that are Logarithmic in the Dimension
, 2007
"... We design an online algorithm for Principal Component Analysis. In each trial the current instance is centered and projected into a probabilistically chosen low dimensional subspace. The regret of our online algorithm, i.e. the total expected quadratic compression loss of the online algorithm minus ..."
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Cited by 24 (3 self)
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We design an online algorithm for Principal Component Analysis. In each trial the current instance is centered and projected into a probabilistically chosen low dimensional subspace. The regret of our online algorithm, i.e. the total expected quadratic compression loss of the online algorithm minus the total quadratic compression loss of the batch algorithm, is bounded by a term whose dependence on the dimension of the instances is only logarithmic. We first develop our methodology in the expert setting of online learning by giving an algorithm for learning as well as the best subset of experts of a certain size. This algorithm is then lifted to the matrix setting where the subsets of experts correspond to subspaces. The algorithm represents the uncertainty over the best subspace as a density matrix whose eigenvalues are bounded. The running time is O(n²) per trial, where n is the dimension of the instances.
Proximity function minimization using multiple Bregman projections, with applications to split feasibility and KullbackLeibler distance minimization
 Annals of Operations Research
, 2001
"... Abstract. Problems in signal detection and image recovery can sometimes be formulated as a convex feasibility problem (CFP) of finding a vector in the intersection of a finite family of closed convex sets. Algorithms for this purpose typically employ orthogonal or generalized projections onto the in ..."
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Abstract. Problems in signal detection and image recovery can sometimes be formulated as a convex feasibility problem (CFP) of finding a vector in the intersection of a finite family of closed convex sets. Algorithms for this purpose typically employ orthogonal or generalized projections onto the individual convex sets. The simultaneous multiprojection algorithm of Censor and Elfving for solving the CFP, in which different generalized projections may be used at the same time, has been shown to converge for the case of nonempty intersection; still open is the question of its convergence when the intersection of the closed convex sets is empty. Motivated by the geometric alternating minimization approach of Csiszár and Tusnády and the product space formulation of Pierra, we derive a new simultaneous multiprojection algorithm that employs generalized projections of Bregman to solve the convex feasibility problem or, in the inconsistent case, to minimize a proximity function that measures the average distance from a point to all convex sets. We assume that the Bregman distances involved are jointly convex, so that the proximity function itself is convex. When the intersection of the convex sets is empty, but the closure of the proximity function has a unique global minimizer, the sequence of iterates converges to this unique minimizer. Special cases of this algorithm include the “Expectation Maximization Maximum Likelihood ” (EMML) method in emission tomography and a new convergence result for an algorithm that solves the split feasibility problem.
Infimal convolution regularizations with discrete l1type functionals
 Comm. Math. Sci
, 2011
"... Dedicated to Prof. Dr. Lothar Berg on the occasion of his 80th birthday ..."
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Dedicated to Prof. Dr. Lothar Berg on the occasion of his 80th birthday
Proximal point methods for quasiconvex and convex functions with Bregman distances on Hadamard manifolds
 J. Convex Anal
, 2009
"... This paper generalizes the proximal point method using Bregman distances to solve convex and quasiconvex optimization problems on noncompact Hadamard manifolds. We will proved that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we obta ..."
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Cited by 23 (3 self)
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This paper generalizes the proximal point method using Bregman distances to solve convex and quasiconvex optimization problems on noncompact Hadamard manifolds. We will proved that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we obtain the same convergence properties for the classical proximal method, applied to a class of quasiconvex problems. Finally, we give some examples of Bregman distances in nonEuclidean spaces.
A massively parallel algorithm for nonlinear stochastic network problems
 Operations Research
, 1993
"... We develop an algorithm for solving nonlinear twostage stochastic problems with network recourse. The algorithm is based on the framework of rowaction methods. The problem is formulated by replicating the firststage variables and then adding nonanticipativity side constraints. A series of (indep ..."
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Cited by 23 (7 self)
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We develop an algorithm for solving nonlinear twostage stochastic problems with network recourse. The algorithm is based on the framework of rowaction methods. The problem is formulated by replicating the firststage variables and then adding nonanticipativity side constraints. A series of (independent) deterministic network problems are solved at each step of the algorithm, followed by an iterative step over the nonanticipativity constraints. The solution point of the iterates over the nonanticipativity constraints can be obtained analytically. The rowaction nature of the algorithm makes it suitable for parallel implementations. A data representation of the problem is developed that permits the massively parallel solution of all the scenario subproblems concurrently. The algorithm is implemented on a Connection Machine CM2 with up to 32K processing elements and achieves computing rates of 250 MFLOPS. Very large problems 8192 scenarios with a deterministic equivalent nonlinear program with 1,272,160 variables and 495,616 constraints are solved within a few minutes. We report extensive numerical results regarding the effects
A survey on the continuous nonlinear resource allocation problem
 Eur. J. Oper. Res
, 2008
"... Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering a ..."
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Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering and economic sciences, through resource allocation and balancing problems in manufacturing, statistics, military operations research and production and financial economics, to subproblems in algorithms for a variety of more complex optimization models. This paper surveys the history and applications of the problem, as well as algorithmic approaches to its solution. The most common techniques are based on finding the optimal value of the Lagrange multiplier for the explicit constraint, most often through the use of a type of line search procedure. We analyze the most relevant references, especially regarding their originality and numerical findings, summarizing with remarks on possible extensions and future research. 1 Introduction and
Asymptotic behavior of relatively nonexpansive operators in Banach spaces
 J. Appl. Anal
"... Abstract. Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K. We consider complete metric spaces of selfmappings of K which fix all the points of F and are relatively nonexpansive with respect to a given convex function f on X. We prove (under cert ..."
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Abstract. Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K. We consider complete metric spaces of selfmappings of K which fix all the points of F and are relatively nonexpansive with respect to a given convex function f on X. We prove (under certain assumptions on f) that the iterates of a generic mapping in these spaces converge strongly to a retraction onto F. In this paper we consider the problem of whether and under what conditions, relatively nonexpansive operators T defined on, and with values in, a nonempty, closed convex subset K of a Banach space (X,   · ) have the