We introduce a method that aims to find the global minimum of a continuous nonconvex function on a compact subset of R^d. It is assumed that function evaluations are expensive and that no additional information is available. Radial basis function interpolation is used to define a utility function. The maximizer of this function is the next point where the objective function is evaluated. We show that, for most types of radial basis functions that are considered in this paper, convergence can be achieved without further assumptions on the objective function. Besides, it turns out that our method is closely related to a statistical global optimization method, the P-algorithm. A general framework for both methods is presented. Finally, a few numerical examples show that on the set of Dixon-Szego test functions our method yields favourable results in comparison to other global optimization methods.

INTRODUCTION In this paper we consider Simulated Annealing algorithms (SA in what follows) applied to continuous global optimization problems, i.e. problems with the following form f = min x2X f(x); (1.1) where X ` ! n is a continuous domain, often assumed to be compact, which, combined with the continuity or lower semicontinuity of f , guarantees the existence of the minimum value f . SA algorithms are based on an analogy with a physical phenomenon: while at high temperatures the molecules in a liquid move freely, if the temperature is slowly decreased the thermal mobility of the molecules is lost and they form a pure crystal which also corresponds to a state of minimum energy. If the temperature is decreased too quickly (the so called quenching) a liquid metal rather ends up in a polycrystalline or amorphous state with

. In this paper we propose a form of the DIRECT algorithm that is strongly biased toward local search. This form should do well for small problems with a single global minimizer and only a few local minimizers. We motivate our formulation with some results on how the original formulation of the DIRECT algorithm clusters its search near a global minimizer. We report on the performance of our algorithm on a suite of test problems and observe that the algorithm performs particularly well when termination is based on a budget of function evaluations. Key words. DIRECT, local clustering, local bias 1. Introduction. The DIRECT (DIviding RECTangles) algorithm [13, 14] is a pattern search method (in the sense of [17]) that balances local and global search in a attempt to efficiently find a global optimizer. Other deterministic sampling methods, such as implicit filtering [9, 15], MDS [6], Hooke-Jeeves [10], or Nelder-Mead [16], drive an approximate gradient to zero and are not designed for g...

In recent years, the multimedia retrieval community is gradually shifting its emphasis from analyzing one media source at a time to exploring the opportunities of combining diverse knowledge sources from correlated media types and context. This thesis presents a conditional probabilistic retrieval model as a principled framework to combine diverse knowledge sources. An efficient rank-based learning approach has been developed to explicitly model the ranking relations in the learning process. Under this retrieval framework, we overview and develop a number of state-of-the-art approaches for extracting ranking features from multimedia knowledge sources. To incorporate query information in the combination model, this thesis develops a number of query analysis models that can automatically discover mixing structure of the query space based on previous retrieval results. To adapt the combination function on a per query basis, this thesis also presents a probabilistic local context analysis(pLCA) model to automatically leverage additional retrieval sources to improve initial retrieval outputs. All the proposed approaches are evaluated on multimedia retrieval tasks with large-scale video collections as well as meta-search tasks with large-scale text collections. 1

video retrieval?

this paper |produces a user-speci ed number of suggested evaluation points in each step; |proceeds by successive partitioning of the box (branch) and building local quadratic models ( t); |combines local and global search and allows the user to determine which of both should be emphasized; |handles local search from the best point with the aid of trust regions; |allows for hidden constraints and assigns to such points a function value based on the function values of nearby feasible points

Combining search results from multimedia sources is crucial for dealing with heterogeneous multimedia data, particularly in multimedia retrieval where a final ranked list of items of interest is returned sorted by confidence or relevance. However, relatively little attention has been given to combination functions, especially their upper bound performance limits. This paper presents a theoretical framework for studying upper bounds for two types of combination functions. A general upper bound and two approximations are proposed for monotonic combination functions. We also studied the upper bounds for linear combination functions using a global optimization technique. Our experimental results show that the choice of combination functions has a considerable influence to retrieval performance. 1.

Abstract We describe a numerical procedure to obtain bounds on the distribution function of a sum of n dependent risks having fixed marginals. With respect to the existing literature, our method provides improved bounds and can be applied also to large non-homogeneous portfolios of risks. As an application, we compute the VaR-based minimum capital requirement for a portfolio of operational risk losses. Key words risk aggregation – dependency bounds – operational risk – mass transportation duality theorem – global optimization

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this paper, we extend the nearest Kronecker product technique to approximate the Q matrix for a SAN with a Kronecker product, A1 A2 AN . Then, we take M = A 1 2 N as our SAN NKP preconditioner. Copyright c 2003 John Wiley & Sons, Ltd. 1.