set partition by globally optimized cluster seed points abstract a new method is proposed for solving set partition clustering problems the suggested approach is based on the application of global optimization methodology for selecting best cluster seed points the applicability of the method is illustrated by numerical examples

an approximate approach of global optimization for polynomial programming problems abstract many methods for solving polynomial programming problems can only find locally optimal solutions this paper proposes a method for finding the approximately globally optimal solutions of polynomial programs representing a bounded continuous variable x i as the addition of a discrete variable d i and a small variable i a polynomial term x i x i can be expanded as the sum of d i x j d j i and i j a procedure is then developed to fully linearize d i x j and d j e i and to approximately linearize i j with an error below a pre specified tolerance this linearization procedure can also be extended to higher order polynomial programs several polynomial programming examples in the literature are tested to demonstrate that the proposed method can systematically solve these examples to find the global optimum within a pre specified error

global optimization and simulated annealing in this paper we are concerned with global optimization which can be defined as the problem of finding points on a bounded subset of n in which some real valued functionf assumes its optimal maximal or minimal value we present a stochastic approach which is based on the simulated annealing algorithm the approach closely follows the formulation of the simulated annealing algorithm as originally given for discrete optimization problems the mathematical formulation is extended to continuous optimization problems and we prove asymptotic convergence to the set of global optima furthermore we discuss an implementation of the algorithm and compare its performance with other well known algorithms the performance evaluation is carried out for a standard set of test functions from the literature

a statistical estimate of the structure of multi extremal problems the solution of ak extremal problem is defined as the set of pairs xi i i 1 k where xt isith local minimum and i is the volume of the set of attraction of this minimum a bayesian estimate ofk and 1 k is constructed

a simulated annealing driven multi start algorithm for bound constrained global optimization a derivative free simulated annealing driven multi start algorithm for continuous global optimization is presented we first propose a trial point generation scheme in continuous simulated annealing which eliminates the need for the gradient based trial point generation we then suitably embed the multi start procedure within the simulated annealing algorithm we modify the derivative free pattern search method and use it as the local search in the multi start procedure we study the convergence properties of the algorithm and test its performance on a set of 50 problems numerical results are presented which show the robustness of the algorithm numerical comparisons with a gradient based simulated annealing algorithm and three population based global optimization algorithms show that the new algorithm could offer a reasonable alternative to many currently available global optimization algorithms specially for problems requiring direct search type algorithm

numerical simulation on hyperbolic diffusion equations using modified cubic b spline differential quadrature methods in this article a modified cubic b spline differential quadrature method mcb dqm is proposed to solve a hyperbolic diffusion problem in which flow motion is affected by both convection and diffusion one dimensional hyperbolic non homogeneous heat wave and telegraph equations are also considered along with two dimensional hyperbolic diffusion problem the method reduces the hyperbolic problem into a system of nonlinear ordinary differential equations the system is then solved by the optimal four stage three order strong stability preserving time stepping runge kutta ssp rk43 scheme the reliability and efficiency of the method has been tested on seven examples the stability of the method is also discussed and found to be unconditionally stable

minimum energy point charge configurations on a circular disk stochastic global optimization methods are used together with problem specific heuristics to find configurations of n equal point charges on a circular disk such that the potential energy is minimized previous such optimal or conjecturally optimal configurations have been published only for and n 29 30 50 earlier results are examined and the best currently known configurations most of them new for are presented

applying electromagnetism like mechanism for feature selection in recent years methods of feature selection have been increasingly emphasized as venues for reducing cost and shortening the length of time required for computation in data mining this study utilizes electromagnetism like mechanism as a wrapper approach to feature selection birbil and fang proposed em in 2003 em uses the attraction repulsion mechanism of the electromagnetism theory to ascertain the optimal solution although em has been applied to the topic of optimization in continuous space and a small number of studies on discrete problems it has not been applied to the subject of feature selection in this study em combined with 1 nearest neighbor 1nn was applied for feature selection and classification this study utilized the total force exerted on a particle and evaluated this force to determine which features are to be selected the most crucial features were selected according to the proposed method based on the minimum miss classification rate which was attained through 1nn an unknown datum was classified by 1nn based on the chosen reduced model to estimate the effectiveness of the proposed method a numerical experiment was conducted using several data sets with diverse sizes features separability and classes experimental results indicated that the proposed method outperformed other well known algorithms in not only balanced classification accuracy but also efficiency of feature selection lastly this study used an actual case concerning gestational diabetes mellitus to demonstrate the workability of the proposed method

stochastic global optimization methods part 1 clustering methods in this stochastic approach to global optimization clustering techniques are applied to identify local minima of a real valued objective function that are potentially global three different methods of this type are described their accuracy and efficiency are analyzed in detail

the application of a unified bayesian stopping criterion in competing parallel algorithms for global optimization abstract the unconstrained global programming problem is addressed using a multistart multialgorithminfrastructure in which different algorithms compete in parallel for a contribution towards a single global stopping criterion denoted the unified bayesian global stopping criterion the use of different algorithms is motivated by the observation that no single global optimization algorithm consistently outperforms all other algorithms when applied to large sets of problems from different classes the bayesian stopping criterion is based on the single assumption that the probability of each algorithm converging to the global optimum is at least as large as the probability of convergence to any other local minimum this assumption is often valid in the case of practical problems of physical origin e g determining physical configurations corresponding to minimum potential energy results for parallel clusters of up to 128 machines are presented

stochastic global optimization methods part 11 multi level methods in part ii of our paper two stochastic methods for global optimization are described that with probability 1 find all relevant local minima of the objective function with the smallest possible number of local searches the computational performance of these methods is examined both analytically and empirically

some old traditions in mathematics and in mathematical education abstract continuing the discussion by azbelev about the harmful influence of some classical traditions on the study of differential equations 1 this note presents further instances of old traditions and of their impact on the development of certain areas of mathematics and its applications

a stochastic method for global optimization a stochastic method for global optimization is described and evaluated the method involves a combination of sampling clustering and local search and terminates with a range of confidence intervals on the value of the global optimum computational results on standard test functions are included as well

application of the multilevel single linkage method to one dimensional electromagnetic inverse scattering problem an inverse scattering method for the reconstruction of the permittivity and conductivity profiles of a multilayered medium and for that of the impedance profile of a nonuniform transmission line is proposed the inversion is based on the global minimization of an objective function by the multilevel single linkage method the objective function is defined as the mean square error between the measured data and the data obtained from the solution of the forward problem an exact formulation for the gradient of the objective function in closed form is derived the necessary condition for the unique solution of the inverse problem of a nonuniform transmission line is discussed reconstruction examples using both experimental and noisy synthetic data are presented

on the mixed integer signomial programming problems this paper proposes an approximate method to solve the mixed integer signomial programming problem for which the objective function and the constraints may contain product terms with exponents and decision variables which could be continuous or integral a linear programming relaxation is derived for the problem based on piecewise linearization techniques which first convert a signomial term into the sum of absolute terms these absolute terms are then linearized by linearization strategies in addition a novel approach is included for solving integer and undefined problems in the logarithmic piecewise technique which leads to more usefulness of the proposed method the proposed method could reach a solution as close as possible to the global optimum

global optimization of statistical functions with simulated annealing abstract many statistical methods rely on numerical optimization to estimate a model s parameters unfortunately conventional algorithms sometimes fail even when they do converge there is no assurance that they have found the global rather than a local optimum we test a new optimization algorithm simulated annealing on four econometric problems and compare it to three common conventional algorithms not only can simulated annealing find the global optimum it is also less likely to fail on difficult functions because it is a very robust algorithm the promise of simulated annealing is demonstrated on the four econometric problems

support vector hazards machine a counting process framework for learning risk scores for censored outcomes learning risk scores to predict dichotomous or continuous outcomes using machine learning approaches has been studied extensively however how to learn risk scores for time to event outcomes subject to right censoring has received little attention until recently existing approaches rely on inverse probability weighting or rank based regression which may be inefficient in this paper we develop a new support vector hazards machine svhm approach to predict censored outcomes our method is based on predicting the counting process associated with the time to event outcomes among subjects at risk via a series of support vector machines introducing counting processes to represent time to event data leads to a connection between support vector machines in supervised learning and hazards regression in standard survival analysis to account for di erent at risk populations at observed event times a time varying offset is used in estimating risk scores the resulting optimization is a convex quadratic programming problem that can easily incorporate nonlinearity using kernel trick we demonstrate an interesting link from the profiled empirical risk function of svhm to the cox partial likelihood we then formally show that svhm is optimal in discriminating covariate specific hazard function from population average hazard function and establish the consistency and learning rate of the predicted risk using the estimated risk scores simulation studies show improved prediction accuracy of the event times using svhm compared to existing machine learning methods and standard conventional approaches finally we analyze two real world biomedical study data where we use clinical markers and neuroimaging biomarkers to predict age at onset of a disease and demonstrate superiority of svhm in distinguishing high risk versus low risk subjects

an efficient algorithm for large scale global optimization of continuous functions a fast descent algorithm resorting to a stretching function technique and built on one hybrid method grsa which combines simulated annealing sa algorithm and gradient based methods for large scale global optimizations is proposed unlike the previously proposed method in which the original objective functions remain unchanged during the whole course of optimization the new method firstly constructs an auxiliary function on one local minimizer obtained by gradient based methods and then sa is executed on this constructed auxiliary function instead of on the original objective function in order that we can improve the jumping ability of sa algorithm to escape from the currently discovered local minimum to a better one from which the gradient based methods restart a new local search the above procedure is repeated until a global minimum is detected in addition corresponding to the adopted stretching technique a new next trial point generating scheme is designed it is verified by simulation especially on large scale problems that the convergence speed is greatly accelerated which is its main difference from many other reported methods that mostly cope with functions with less than 50 variables and does not apply to large scale optimization problems furthermore the new algorithm functions as a global optimization procedure with a high success probability and high solution precision

the globally convexized filled functions for global optimization a new filled function the globally convexized filled function is proposed the value of this function tends to positive infinity as the norm of the variable vector tends to infinity and it has no stationary point in the region in which the objective function value is greater than or equal to the least value found so far but it does have a minimizer not only along the radius direction from the minimizer with the least objective function value found so far like filled function found earlier by ge in the region in which the objective function value is less than the least value found so far but with a prefixed minimizer how to adjust parameters in the filled function is considered such a filled function can be appropriately combined with stochastic stopping rules proposed by boender rinnooy kan and timmer the computational results show that this algorithm is quite efficient and reliable

random linkage a family of acceptance rejection algorithms for global optimisation this paper introduces a new infinite class of stochastic algorithms for the optimization of multimodal functions defined over a compact set the main idea is that of generalizing some well known methods inspired by clustering techniques which make use of local search routines started at selected points in a random sample it is shown that there exist interesting classes of global optimization algorithms all possessing the following theoretical properties convergence to the global optimum with probability 1 detection of the global optimum in a finite number of iterations w p 1 probability of starting a local search decreasing to 0 total number of local searches performed even if the algorithm is run forever finite w p 1

minimization by random search techniques we give two general convergence proofs for random search algorithms we review the literature and show how our results extend those available for specific variants of the conceptual algorithm studied here we then exploit the convergence results to examine convergence rates and to actually design implementable methods finally we report on some computational experience

adaptive lqg control of input output systems a cost biased approach in this paper we consider linear systems in input output form and introduce a new adaptive linear quadratic gaussian lqg control scheme which is shown to be self optimizing the identification algorithm incorporates a cost biasing term which favors the parameters with smaller lqg optimal cost and a second term that aims at moderating the time variability of the estimate the corresponding closed loop scheme is proven to be stable and to achieve an asymptotic lqg cost equal to the one obtained under complete knowledge of the true system self optimization the results of this paper extend in a nontrivial way previous results established along the cost biased approach in other settings

mean shift mode seeking and clustering mean shift a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper this generalization makes some k means like clustering algorithms its special cases it is shown that mean shift is a mode seeking process on the surface constructed with a shadow kernal for gaussian kernels mean shift is a gradient mapping convergence is studied for mean shift iterations cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data applications in clustering and hough transform are demonstrated mean shift is also considered as an evolutionary strategy that performs multistart global optimization