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Topic: Global optimum

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	Global Optimization
		A typical result of a global optimization task might be something like “after a one hour search, point P has the highest probability of being the global optimum of error function F in region R”.
		One simple global optimization scheme is the grid search: the merit function M is evaluated at points on a regular grid aligned to the coordinate axes, and the sample with the lowest value of M is taken as an estimate of the global minimum.
		Simulated annealing belongs to a class of global optimizers that are called controlled random search methods because the merit-function space is sampled randomly according to a scheme in which the values of several parameters determine the distribution of the random samples.
	www.sinopt.com /learning1/desnotes/globopt.htm (2543 words)

	Global optimum - Wikipedia, the free encyclopedia
		In mathematics, a global optimum is a selection from a given domain which yields either the highest value or lowest value (depending on the objective), when a specific function is applied.
		By contrast, a local optimum is a selection for which neighboring selections yield values that are not greater.
		The concept of a local optimum implies that the domain is a metric space or topological space, in order that the notion of "neighborhood" should be meaningful.
	en.wikipedia.org /wiki/Global_optimum (188 words)

	Comparing Genetic and Other Search Algorithms (Site not responding. Last check: 2007-10-05)
		For this four-bit function, the global optimum is at 1111, but there are two hill-climbing deceptive optima at 0011 and 1100, the global optimum is 2 bits away from the suboptima.
		For a genetic algorithm using one-point crossover, the probability that the global optimum is found assuming equally fit local optima is roughly the probability that the mates chosen represent the two local optima, multiplied by the probability that crossover produces the global optimum.
		Spaces where recombination of two or more single criterion optima leads toward a global optimum, with a deceptive basin in between to trap hill-climbers, are well suited for genetic algorithms especially when using pareto optimality in their selection process.
	www.cse.unr.edu /~sushil/papers/thesis/thesishtml/node3.html (3341 words)

	It needs to have some exploitation ability
		In evolutionary programming, the global and local exploration abilities are brought in by the mutation and controlled by the variances of the Gaussian random functions employed.
		In order to balance between the global and local exploration abilities and obtain a quick search, the variances can also be encoded into the individuals and therefore evolved simultaneously, as done in evolutionary strategy [10].
		By setting a too small maximum velocity allowed, maximum global exploration ability is limited, and PSO will always favor a local search no matter what the inertia weight is. By setting a large maximum velocity allowed, then the PSO can have a large range of exploration ability to select by selecting the inertia weight.
	www.engr.iupui.edu /~shi/PSO/Paper/EP98/psof6/ep98_pso.html (2478 words)

	Global Partitions - Plastic Laminate Partitions (Site not responding. Last check: 2007-10-05)
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	[No title] (Site not responding. Last check: 2007-10-05)
		In one phase, the population stays in the local optimum forever, and if the population starts with some strings in the global optimum, the final state consists of most of the strings in the local optimum.
		In the second phase, the population evolves to one in which most or all strings are the global optimum.
		In the first phase, a finite population genetic algorithm finds the global optimum much more slowly than simulated annealing, taking a time approximately exponential in the population size to evolve to a population primarily in the global optimum.
	www-cse.ucsd.edu /users/rik/foga4/Abstracts/19-js-abs.txt (297 words)

	ISMP 2000 - Meeting Topics (Site not responding. Last check: 2007-10-05)
		The basic idea for this class of algorithms is to change both the temperature and the radius of the support for the distribution of the next candidate point according to the distance of the current function value from the record value.
		The convergence w.p.1 to the global optimum of algorithms in this class is proved and, under the simplifying assumption of a known global minimum value, also the convergence rate is given.
		It is shown that often, by appropriately choosing some parameters, depending on the behaviour of the objective function in a neighborhood of the global optimum, the convergence rate can be made polynomial with respect to the inverse of the required precision.
	www.isye.gatech.edu /ismp2000/schedule/session_pages/TUC-13-IC119.html (307 words)

	Optimization Online - A Population Based Approach for Hard Global Optimization Problems Based on Dissimilarity Measures
		In this situation, lacking any possibility of guaranteeing global optimality for most problem instances, it is quite difficult to establish rules for discriminating among different algorithms.
		We think that in order to judge the quality of new global optimization methods, different criteria might be adopted like, e.g.: 1) efficiency - measured in terms of the computational effort necessary to obtain the putative global optimum 2) robustness - measured in terms of ``percentage of successes'', i.e.
		In this paper we present a computational framework based on a population-based stochastic method in which different candidate solutions for a single problem are maintained in a population which evolves in such a way as to guarantee a sufficient diversity among solutions.
	www.optimization-online.org /DB_HTML/2005/02/1056.html (294 words)

	Solutions to exercises on on conditions under which a stationary point is a global optimum
		Thus (0, 0, 0) is a global maximizer.
		Since f is convex, this is the global minimizer of f (and there are no other maximizers or minimizers).
		Since the objective function is concave, this input combination is the one that globally maximizes the firm's profit.
	www.chass.utoronto.ca /~osborne/MathTutorial/GOPX1S.HTM (1204 words)

	GOTI: Global Optimization Theory Institute
		In many cases, local optima are physically meaningless, and finding the global optimum becomes a necessity.
		Unfortunately, the task of finding a global optimum is very difficult because standard optimization solvers usually get trapped in local optima.
		The aim of this workshop is to bring together experts from different areas that have contributed to global optimization.
	www-unix.mcs.anl.gov /~leyffer/goti (90 words)

	Citebase - Application of Chaos Induced Near-Resonance Dynamics to Locate the Global Optimum of Functions (Site not responding. Last check: 2007-10-05)
		The problem of locating the global optimum of functions is studied in a dynamic setting.
		When the magnitude of the forcing signal decays slowly, it is shown that the system attains an equilibrium state, which corresponds to the global optimum of the corresponding multimodal potential function.
		The role of bifurcations in facilitating the approach to the global optimum is discussed.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:nlin/0107017 (155 words)

	[No title]
		Global convergence, however, needs to be guaranteed by the global-scope algorithm component which — theoretically — should be used in a complete, 'exhaustive' fashion.
		This approach is designed to generate efficient approximations to the global minimum of a multiextremal function, by fitting a convex function to the set of all known (calculated) local minima.
		GLOBAL can be used for the solution of the general bound-constrained GOP which has a (measurable) real objective function.
	plato.la.asu.edu /gom.html (4411 words)

	Earth Science Websites (Site not responding. Last check: 2007-10-05)
		The optimum interpolation (OI) sea surface temperature (SST) analysis is produced weekly on a one-degree grid.
		Data set include monthly mean gridded, global SSTs from 1870 to present and Sea Ice coverage from 1870 to present.
		The HADRT data are global radiosonde gridded temperature anomalies at standard levels in the troposphere and in the lower stratosphere from 1958 to present.The data are Deg.
	www.science.gmu.edu /~yxing/text/es/data.html (530 words)

	Robotics Institute: Global Optimum Path Planning for a Redundant Space Robot
		This paper presents a global optimum path planning scheme for redundant space robotic manipulators to be used in such missions.
		Two optimum path planning problems are considered: first, given the end-effector trajectory, find the optimum trajectories of the joints, and second, given the terminal conditions of the end-effector, find the optimum trajectories for the end-effector and the joints.
		It is explicitly assumed that the gravity is zero in, and the robotic manipulator is mounted on a completely free-flying base (spacecraft) and the attitude control (reaction wheels or thrust jets) is off.
	www.ri.cmu.edu /pubs/pub_259_text.html (440 words)

	Generation5 Forum - NN - finding global optimum?
		Tried different numbers neurons in hidden layer and already with around 4-6 neurons i got quite good results.
		My problem is that there are a lot of local optimums and with reteaching my net again it gives quite different results each time.
		Another alternative is swapping backprop for some other weight-change algorithm (such as simulated annealing).
	www.generation5.org /forums/topic.asp?TOPIC_ID=658 (160 words)

	Global Optimum Protein Threading with Gapped Alignment and Empirical Pair Score Functions - Lathrop, Smith ... (Site not responding. Last check: 2007-10-05)
		Global Optimum Protein Threading with Gapped Alignment and Empirical Pair Score Functions (1996)
		Abstract: We describe a branch-and-bound search algorithm for finding the exact global optimum gapped sequencestructure alignment ("threading") between a protein sequence and a protein core or structural model, using an arbitrary amino acid pair score function (e.g., contact potentials, knowledge-based potentials, potentials of mean force, etc.).
		Lathrop and T. Smith, Global optimum protein threading with gapped alignment and empirical pair score functions, J. Mol.
	citeseer.ist.psu.edu.cob-web.org:8888 /415162.html (1095 words)

	CEF 1997: Global Optimization Methods for Estimating GARCH Models (Site not responding. Last check: 2007-10-05)
		When they do converge there is no guarantee that the result will be the global rather than a local optimum.
		Research in global optimization methods has resulted in techniques that show promise in locating the desired optimum.
		The best current optimum may be a local rather than global optimum.
	bucky.stanford.edu /cef97/abstracts/jerrell.html (339 words)

	Medieval Warm Period - Wikipedia, the free encyclopedia
		The Medieval Warm Period (MWP) or Medieval Climate Optimum was a time of unusually warm climate in Europe, lasting from about the 10th century to about the 14th century.
		The MWP is often invoked in contentious discussions of global warming and the greenhouse effect.
		The period was followed by the Little Ice Age, a period of cooling that lasted until the 19th century when the current period of global warming began.
	en.wikipedia.org /wiki/Medieval_climate_optimum (896 words)

	3/7/96 Christodoulos A. Floudas (Site not responding. Last check: 2007-10-05)
		In the last decade the area of global optimization has attracted a lot of attention from a variety of disciplines that include all branches of engineering, operations research, applied mathematics, computational chemistry, and biology.
		Third, the global optimum solution may have a very different physical interpretation when it is compared to local solutions.
		These methods (i) offer theoretical guarantee of attaining an epsilon-global optimum solution in a finite number of iterations, (ii) provide valid lower and upper bounds on the global solution, and (iii) identify local optima close to the global minimum.
	www.cs.jhu.edu /~cowen/Seminars/floudas.html (305 words)

	Conditions under which a stationary point is a global optimum (Site not responding. Last check: 2007-10-05)
		Thus the global minimizer of the function is (0, 0); the minimum value of the function is 3.
		Thus we cannot conclude that (0, 0) is either a global maximizer or minimizer.
		Hence its unique global minimizer is (0, 0, 0), with a value of 0.
	www.chass.utoronto.ca /~osborne/MathTutorial/GOP.HTM (993 words)

	Global optimization - Wikipedia, the free encyclopedia
		Global optimization is a branch of applied mathematics and numerical analysis that deals with the optimization of a function or a set of functions to some criteria.
		Finding the global maximum or minimum of a function is a lot more challenging and has been impossible for many problems so far.
		The effective energy transformation scheme as a special continuation approach to global optimization with application to molecular conformation.
	en.wikipedia.org /wiki/Global_optimization (322 words)

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	Hybrid Global Optimization Algorithms for Protein Structure Prediction: Alternating Hybrids -- Klepeis et al. 84 (2): ...
		The domain is first bisected, and the minima of the convex underestimators in the two subdomains are located at 1 and 2.
		At this point, the upper and lower bounds converge at point 7—this point is higher in energy than 5, but lower in energy than 6, meaning that it represents both the upper and lower bound on the system.
		This indicates that 7 is the global optimum solution.
	www.biophysj.org /cgi/content/full/84/2/869 (8519 words)

	[No title] (Site not responding. Last check: 2007-10-05)
		Assume that a local optimum has been found and it is desired to test the hypothesis that it is a global optimum.
		SUBROUTINE GLOB1 evaluates the function to be optimized n times randomly in a region specified by the user and tests the hypothesis that the previous local optimum is global.
		One hopes that this occurs near the global optimum.
	www.quandt.com /handbook710/16.htm (1472 words)

	Search Global Optimum Solutions for Large Scale Nonconvex NLP Problems in Water Resources Management Modeling
		In this paper, we apply the Generalized Benders Decomposition (GBD) algorithm to two large nonconvex water resources models involving reservoir operations and water allocation in a river basin, using an approximation to the GBD cuts proposed by Floudas et.
		Methods for obtaining global solutions to nonconvex mathematical programming problems have not appeared frequently in the water resources literature, even though these problems are often unavoidable in water resources management modeling.
		There is no known polynomially bounded algorithm for solving the reverse convex RMP(r) globally, and GBD cannot guarantee a global solution of the original problem without such a guarantee for RMP(r).
	www.utexas.edu /courses/lasdon/solving.htm (4908 words)

	Amazon.com: State of the Art in Global Optimization: Computational Methods and Applications (Nonconvex Optimization and ... (Site not responding. Last check: 2007-10-05)
		In many of these problems it is necessary to compute the global optimum (or a good approximation) of a multivariable function.
		Global optimization problems belong to the complexity class of NP-hard problems.
		Global optimization has received a lot of attention in the past ten years, due to the success of new algorithms for solving large classes of problems from diverse areas such as computational chemistry and biology, structural optimization, computer sciences, operations research, economics, and engineering design and control.
	www.amazon.com /State-Global-Optimization-Computational-Applications/dp/0792338383 (810 words)

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	Global Versus Local Optima
		The smallest local minimum of an objective function is called the global minimum, and the largest local maximum of an objective function is called the global maximum.
		Hence, the subroutines may occasionally fail to find the global optimum.
		One way to find out whether the objective function has more than one local optimum is to run various optimizations with a pattern of different starting points.
	www.asu.edu /it/fyi/dst/helpdocs/statistics/sas/sasdoc/sashtml/iml/chap11/sect4.htm (392 words)

	CASL Home Page - C. A. Floudas - Process Synthesis; ProcessControl; Mixed-Integer Nonlinear and Global Optimization; ...
		Liu W.B. and C.A. Floudas, "A Remark on the GOP Algorithm for Global Optimization", Journal of Global Optimization, Vol.
		PDF (7341K)), "Deterministic Global Optimization for Protein Structure Prediction", Chapter in Advances in Convex Analysis and Global Optimization, a Book in honor of C. Caratheodory, N. Hadjisavvas and P.M. Pardalos (Eds.), 31-74 (2001).
		Klepeis J.L. and C.A. Floudas, "ASTRO-FOLD: a combinatorial and global optimization framework for ab initio prediction of three-dimensional structures of proteins from the amino acid sequence", Biophysical Journal, 85, 2119-2146 (2003).
	titan.princeton.edu /publications.htm (6724 words)

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