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214
Optimization by direct search: New perspectives on some classical and modern methods
 SIAM Review
, 2003
"... Abstract. Direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives. Direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because t ..."
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Cited by 126 (14 self)
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Abstract. Direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives. Direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis. Nonetheless, users remained loyal to these methods, most of which were easy to program, some of which were reliable. In the past fifteen years, these methods have seen a revival due, in part, to the appearance of mathematical analysis, as well as to interest in parallel and distributed computing. This review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited. Our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results. The underlying principles allow generalization to handle bound constraints and linear constraints. We also discuss extensions to problems with nonlinear constraints.
Direct search methods: then and now
, 2000
"... We discuss direct search methods for unconstrained optimization. We give a modern perspective on this classical family of derivativefree algorithms, focusing on the development of direct search methods during their golden age from 1960 to 1971. We discuss how direct search methods are characterized ..."
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Cited by 66 (4 self)
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We discuss direct search methods for unconstrained optimization. We give a modern perspective on this classical family of derivativefree algorithms, focusing on the development of direct search methods during their golden age from 1960 to 1971. We discuss how direct search methods are characterized by the absence of the construction of a model of the objective. We then consider a number of the classical direct search methods and discuss what research in the intervening years has uncovered about these algorithms. In particular, while the original direct search methods were consciously based on straightforward heuristics, more recent analysis has shown that in most — but not all — cases these heuristics actually
Convergence of the NelderMead simplex method to a nonstationary point
 SIAM J. Optim
, 1996
"... . This paper analyses the behaviour of the NelderMead simplex method for a family of examples which cause the method to converge to a nonstationary point. All the examples use continuous functions of two variables. The family of functions contains strictly convex functions with up to three continu ..."
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Cited by 53 (0 self)
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. This paper analyses the behaviour of the NelderMead simplex method for a family of examples which cause the method to converge to a nonstationary point. All the examples use continuous functions of two variables. The family of functions contains strictly convex functions with up to three continuous derivatives. In all the examples the method repeatedly applies the inside contraction step with the best vertex remaining fixed. The simplices tend to a straight line which is orthogonal to the steepest descent direction. It is shown that this behaviour cannot occur for functions with more than three continuous derivatives. The stability of the examples is analysed. Key words. NelderMead method, direct search, simplex, unconstrained minimization AMS subject classifications. 65K05 1. Introduction. Direct search methods are very widely used in chemical engineering, chemistry and medicine. They are a class of optimization methods which are easy to program, do not require derivatives and a...
Applicationaware Admission Control and Scheduling in Web Servers
, 2002
"... This paper presents an architecture and algorithms for optimizing the performance of web services. For a given service, sessionbased admission control is combined with stagewise request queuing, where the stages represent subtasks within sessions. The scheduling of requests is governed by general ..."
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Cited by 42 (0 self)
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This paper presents an architecture and algorithms for optimizing the performance of web services. For a given service, sessionbased admission control is combined with stagewise request queuing, where the stages represent subtasks within sessions. The scheduling of requests is governed by generalized processor sharing. We present a performance model, relying on online estimation of parameters describing clientserver interaction. A reward function corresponding to the service provider's objective is maximized using techniques for nonlinear optimization. In a case study, we model and optimize the resource sharing at a web server hosting an electronic store. The performance advantages of our approach are quantified numerically, and the robustness to parameter estimation errors is assessed by sensitivity analysis.
Detection And Remediation Of Stagnation In The NelderMead Algorithm Using A Sufficient Decrease Condition
 SIAM J. OPTIM
, 1997
"... The NelderMead algorithm can stagnate and converge to a nonoptimal point, even for very simple problems. In this note we propose a test for sufficient decrease which, if passed for the entire iteration, will guarantee convergence of the NelderMead iteration to a stationary point if the objective ..."
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Cited by 31 (1 self)
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The NelderMead algorithm can stagnate and converge to a nonoptimal point, even for very simple problems. In this note we propose a test for sufficient decrease which, if passed for the entire iteration, will guarantee convergence of the NelderMead iteration to a stationary point if the objective function is smooth. Failure of this condition is an indicator of potential stagnation. As a remedy we propose a new step, which we call an oriented restart, which reinitializes the simplex to a smaller one with orthogonal edges which contains an approximate steepest descent step from the current best point. We also give results that apply when objective function is a lowamplitude perturbation of a smooth function. We illustrate our results with some numerical examples.
Flux Invariants for Shape
 In CVPR
, 2003
"... We consider the average outward flux through a Jordan curve of the gradient vector field of the Euclidean distance function to the boundary of a 2D shape. Using an alternate form of the divergence theorem, we show that in the limit as the area of the region enclosed by such a curve shrinks to zero, ..."
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Cited by 28 (3 self)
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We consider the average outward flux through a Jordan curve of the gradient vector field of the Euclidean distance function to the boundary of a 2D shape. Using an alternate form of the divergence theorem, we show that in the limit as the area of the region enclosed by such a curve shrinks to zero, this measure has very different behaviours at medial points than at nonmedial ones, providing a theoretical justification for its use in the HamiltonJacobi skeletonization algorithm of [7]. We then specialize to the case of shrinking circular neighborhoods and show that the average outward flux measure also reveals the object angle at skeletal points. Hence, formulae for obtaining the boundary curves, their curvatures, and other geometric quantities of interest, can be written in terms of the average outward flux limit values at skeletal points. Thus this measure can be viewed as a Euclidean invariant for shape description: it can be used to both detect the skeleton from the Euclidean distance function, as well as to explicitly reconstruct the boundary from it. We illustrate our results with several numerical simulations. 1.
Modeling TTLbased Internet Caches
, 2002
"... This paper presents a way of modeling the hit rates of caches that use a timetolive (TTL)based consistency policy. TTLbased consistency, as exemplified by DNS and Web caches, is a policy in which a data item, once retrieved, remains valid for a period known as the "timetolive". Cache systems u ..."
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Cited by 22 (0 self)
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This paper presents a way of modeling the hit rates of caches that use a timetolive (TTL)based consistency policy. TTLbased consistency, as exemplified by DNS and Web caches, is a policy in which a data item, once retrieved, remains valid for a period known as the "timetolive". Cache systems using large TTL periods are known to have high hit rates and scale well, but the effects of using shorter TTL periods are not well understood. We model hit rate as a function of request arrival times and the choice of TTL, enabling us to better understand cache behavior for shorter TTL periods. Our formula for the hit rate is closed form and relies upon a simplifying assumption about the interarrival times of requests for the data item in question: that these requests can be modeled as a sequence of independent and identically distributed random variables. Analyzing extensive DNS traces, we find that the results of the formula match observed statistics surprisingly well; in particular, the analysis is able to adequately explain the somewhat counterintuitive empirical finding of Jung et al. [1] that the cache hit rate for DNS accesses rapidly increases as a function of TTL, exceeding 80% for a TTL of 15 minutes.
Dynamic assortment with demand learning for seasonal consumer goods
 MANAGEMENT SCI
, 2007
"... ..."
Kissing Numbers, Sphere Packings, and Some Unexpected Proofs
 NOTICES AMER. MATH. SOC
, 2004
"... ..."
For a recent report
 Core Experiment ROI 1: ROI refinement", ISO/IEC JTC1/SC29/WG1 N990
, 1995
"... Abstract This report gives a report of the developed methods and techniques of multimodal recognizers that are used in the M4 domain. This includes the description of recognizers in the auditory domain, like phoneme recognition and localization, the video domain, represented by gesture recognition, ..."
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Cited by 20 (0 self)
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Abstract This report gives a report of the developed methods and techniques of multimodal recognizers that are used in the M4 domain. This includes the description of recognizers in the auditory domain, like phoneme recognition and localization, the video domain, represented by gesture recognition, person identification, person tracking and gaze tracking, and multimodal multimodal approaches for tracking and localization of people. The outcome of these approaches give a sufficient input for the more higher level approaches in WP3 for efficient meeting analysis and multimodal access. M4 Deliverable D2.2 1