a discrete dynamic convexized method for nonlinear integer programming in this paper we consider the box constrained nonlinear integer programming problem we present an auxiliary function which has the same discrete global minimizers as the problem the minimization of the function using a discrete local search method can escape successfully from previously converged discrete local minimizers by taking increasing values of a parameter we propose an algorithm to find a global minimizer of the box constrained nonlinear integer programming problem the algorithm minimizes the auxiliary function from random initial points we prove that the algorithm can converge asymptotically with probability one numerical experiments on a set of test problems show that the algorithm is efficient and robust

maximum entropy and the nearly black object summary maximum entropy me inversion is a non linear inversion technique for inverse problems where the object to be recovered is known to be positive it has been applied in areas ranging from radio astronomy to various forms of spectroscopy sometimes with dramatic success in some cases me has attained an order of magnitude finer resolution and or an order of magnitude smaller noise level than that obtainable by standard linear methods the dramatic successes all seem to occur in cases where the object to be recovered is nearly black essentially zero in the vast majority of samples we show that near blackness is required both for signal to noise enhancements and for superresolution however other methods in particular minimum 1 norm reconstruction may exploit near blackness to an even greater extent

a filled function method for finding a global minimizer on global integer optimization the paper gives a definition of the filled function for nonlinear integer programming this definition is modified from that of the global convexized filled function for continuous global optimization a filled function with only one parameter which satisfies this definition is presented we also discuss the properties of the proposed function and give a filled function method to solve the nonlinear integer programming problem the implementation of the algorithm on several test problems is reported with satisfactory numerical results

a new filled function for unconstrained global optimization abstract seeking global optima of an unconstrained and multi modal global optimization problem min x f x by constructing a filled function is concerned in this paper on the basis of analyzing filled functions presented before a new filled function is proposed and it is proved to meet the properties of a filled function moreover solutions of numerical experiments show that the function is quite effective

an interval algorithm for nondifferentiable global optimization an interval algorithm for constrained nondifferentiable global optimization in which an exact penalty function is used is described and the determination of the penalty function parameter is discussed numerical results are presented

finding more and more solutions of a system of nonlinear equations this paper is addressed to an old but difficult topic viz how to find more and more solutions of a system of nonlinear equations we find a transformation by using so called locally affective functions to transform the original system to a new system which has not the already found solutions of the original system but only the unfound solutions and so we can find a new solution of the original system through finding a solution of the transformed system we also discuss some likely uses of locally affective functions in the solution of other nonlinear problems

high dimensional asymptotics of prediction ridge regression and classification we provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model we work in a high dimensional asymptotic regime where p n to infty and p n to gamma 0 and allow for arbitrary covariance among the features for both methods we provide an explicit and efficiently computable expression for the limiting predictive risk which depends only on the spectrum of the feature covariance matrix the signal strength and the aspect ratio gamma especially in the case of regularized discriminant analysis we find that predictive accuracy has a nuanced dependence on the eigenvalue distribution of the covariance matrix suggesting that analyses based on the operator norm of the covariance matrix may not be sharp our results also uncover an exact inverse relation between the limiting predictive risk and the limiting estimation risk in high dimensional linear models the analysis builds on recent advances in random matrix theory

a parameter free filled function for unconstrained global optimization the filled function method is considered as an efficient method to find the global minimum of multidimensional functions a number of filled functions were proposed recently most of which have one or two adjustable parameters however there is no efficient criterion to choose the parameter appropriately in this paper we propose a filled function without parameter and this function includes neither exponential terms nor logarithmic terms so it is superior to the traditional ones theories of the filled function are investigated and an algorithm which does not compute gradients during minimizing the filled function is presented moreover the numerical experiments demonstrate the efficiency of the proposed filled function

information theoretic bounds for compressed sensing in this paper we derive information theoretic performance bounds to sensing and reconstruction of sparse phenomena from noisy projections we consider two settings output noise models where the noise enters after the projection and input noise models where the noise enters before the projection we consider two types of distortion for reconstruction support errors and mean squared errors our goal is to relate the number of measurements m and snr to signal sparsity k distortion level d and signal dimension n we consider support errors in a worst case setting we employ different variations of fano s inequality to derive necessary conditions on the number of measurements and snr required for exact reconstruction to derive sufficient conditions we develop new insights on max likelihood analysis based on a novel superposition property in particular this property implies that small support errors are the dominant error events consequently our ml analysis does not suffer the conservatism of the union bound and leads to a tighter analysis of max likelihood these results provide order wise tight bounds for output noise models we show that asymptotically an snr of n together with k n k measurements is necessary and sufficient for exact support recovery furthermore if a small fraction of support errors can be tolerated a constant snr turns out to be sufficient in the linear sparsity regime in contrast for input noise models we show that support recovery fails if the number of measurements scales as o n n snr implying poor compression performance for such cases motivated by the fact that the worst case setup requires significantly high snr and substantial number of measurements for input and output noise models we consider a bayesian setup to derive necessary conditions we develop novel extensions to fano s inequality to handle continuous domains and arbitrary distortions we then develop a new max likelihood analysis over the set of rate distortion quantization points to characterize tradeoffs between mean squared distortion and the number of measurements using rate distortion theory we show that with constant snr the number of measurements scales linearly with the rate distortion function of the sparse phenomena

on random pattern test length the testing of large logic networks with random patterns is examined work by previous workers for single faults is extended to a class of multiple fault situations not only is the problem of fault detection in the presence of nonmasking multiple faults treated but the question of distinguishing between them is also examined it is shown that a test that merely exposes each fault has a high probability of distinguishing between the faults the relationships between quality diagnostic resolution and random pattern test length are developed the results have application to self test schemes that use random patterns as stimuli

a new filled function method for global optimization a new definition of the filled function is presented in this paper based on the definition a new filled function is presented and a global optimization algorithm is developed the implementation of the algorithm on several test problems is reported with satisfactory numerical results the numerical experiments further show that the algorithm may solve higher dimensional global optimization problems

filled function method for nonlinear equations systems of nonlinear equations are ubiquitous in engineering physics and mechanics and have myriad applications generally they are very difficult to solve in this paper we will present a filled function method to solve nonlinear systems we will first convert the nonlinear systems into equivalent global optimization problems with the property x is a global minimizer if and only if its function value is zero a filled function method is proposed to solve the converted global optimization problem numerical examples are presented to illustrate our new techniques

finding global minimizer with one parameter filled function on unconstrained global optimization abstract in this paper a filled function with one parameter is proposed for solving unconstrained global optimization problems this filled function is modified from the previously reported one see paper y j yang y l shang a new filled function method for unconstrained global optimization applied mathematics and computations 173 1 2006 501 512 the properties of the filled function are discussed in this paper an algorithm for unconstrained global optimization is developed from this new filled function the computational results show that this algorithm is efficient and reliable

a integral filter algorithm for unconstrained global optimization abstract in this paper making use of an integral inequality a necessary and sufficient condition is given for a point to be a global minimizer based on the integral inequality a novel integral form algorithm is proposed for unconstrained global optimization it is different from the other deterministic global search algorithm under mild conditions it is proved that in theory a global minimizer of the objective function can be certainly found by the presented algorithm in order to indicate the efficiency and reliability of the method four numerical examples are reported

a new filled function method for unconstrained global optimization in this paper a new filled function which has better properties is proposed for identifying a global minimum point for a general class of nonlinear programming problems within a closed bounded domain an algorithm for unconstrained global optimization is developed from the new filled function theoretical and numerical properties of the proposed filled function are investigated the implementation of the algorithm on seven test problems is reported with satisfactory numerical results

which bridge estimator is the best for variable selection we study the problem of variable selection for linear models under the high dimensional asymptotic setting where the number of observations n grows at the same rate as the number of predictors p we consider two stage variable selection techniques tvs in which the first stage uses bridge estimators to obtain an estimate of the regression coefficients and the second stage simply thresholds this estimate to select the important predictors the asymptotic false discovery proportion operatorname afdp and true positive proportion atpp of these tvs are evaluated we prove that for a fixed atpp in order to obtain a smaller operatorname afdp one should pick a bridge estimator with smaller asymptotic mean square error in the first stage of tvs based on such principled discovery we present a sharp comparison of different tvs via an in depth investigation of the estimation properties of bridge estimators rather than orderwise error bounds with loose constants our analysis focuses on precise error characterization various interesting signal to noise ratio and sparsity settings are studied our results offer new and thorough insights into high dimensional variable selection for instance we prove that a tvs with ridge in its first stage outperforms tvs with other bridge estimators in large noise settings two stage lasso becomes inferior when the signal is rare and weak as a by product we show that two stage methods outperform some standard variable selection techniques such as operatorname lasso and sure independence screening under certain conditions

a class of filled functions for box constrained continuous global optimization in this paper we show that the unconstrained continuous global minimization problem cannot be solved by any algorithm so we consider the box constrained continuous global minimization problem we present a definition of filled function for the problem moreover a new class of filled functions are constructed which contains only one parameter a randomized algorithm is designed to solve the box constrained continuous global minimization problem based on the filled function numerical experiments are presented to show the practicability of the algorithm

the barrier attribute of filled functions a number of filled functions was proposed recently this paper presents a new perspective of the filled functions their barrier attribute more filled functions can be constructed according to this new interpretation two of them are with finite barriers while the remains are with infinite barriers

a filled function method for global optimization a novel filled function with one parameter is suggested in this paper for finding a global minimizer for a general class of nonlinear programming problems with a closed bounded box a new algorithm is presented according to the theoretical analysis the implementation of the algorithm on several test problems is reported with satisfactory numerical results

a revised cut peak function method for box constrained continuous global optimization in this paper we modify the concept of cut peak function given in wang et al y wang w fang t wu a deterministic algorithm of global optimization using cut peak functions technique report in the conference of mathematical programming of china 2006 and then propose a revised cut peak function algorithm for solving box constrained continuous optimization problems the smoothing technique is used to overcome the difficulty arising from the non smoothness of the constructed function by using the exterior penalty function method we find iteratively a better minimizer from the current local minimizer till a global minimizer of the concerned problem is found some preliminary numerical results are reported

inclusion functions and global optimization 11 inclusion functions combined with special subdivision strategies are an effective means of solving the global unconstrained optimization problem although these techniques were determined and numerically tested about ten years ago they are nearly unknown and scarcely used in order to make the role of inclusion functions and subdivision strategies more widespread and transparent we will discuss a related simplified basic algorithm it computes approximations of the global minimum and at the same time bounds the absolute approximation error we will show that the algorithm works and converges under more general assumptions than it has been known hitherto that is only appropriate inclusion functions are expected to exist the number of minimal points finite or infinite is not of importance lipschitz conditions or continuity are not assumed as shown in the appendix the required inclusion functions can be constructed and programmed without difficulty in a natural way using interval analysis

a new extension of piyavskii s method to holder functions of several variables in this paper we suggest a new extension of the method of piyavskii for global optimization of a holder function with exponent 1 1 in the one dimensional case a modification of piyavskii s algorithm is introduced and it is based on the construction of sub estimators which are piecewise linear the algorithm is then some what easily moreover the results we obtain seem interesting in the higher dimension a new variant of the alienor reducing transformation which has been devised for exploiting one dimensional global optimization techniques known for their great efficiency is used the method consists in reducing a multidimensional problem to a one dimensional one using the so called dense curves the convergence of the methods is also studied

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

a filled function method for finding a global minimizer of a function of several variables the concept of a filled function is introduced we construct a particular filled function and analyze its properties an algorithm for global minimization is generated based on the concept and properties of the filled function some typical examples with 1 to 10 variables are tested and computational results show that in most cases this algorithm works better than the tunneling algorithm the advantages and disadvantages are analyzed and further research directions are discussed

a filled function method applied to nonsmooth constrained global optimization the filled function method is an effective approach to find a global minimizer in this paper based on a new definition of the filled function for nonsmooth constrained programming problems a one parameter filled function is constructed to improve the efficiency of numerical computation then a corresponding algorithm is presented it is a global optimization method which modify the objective function as a filled function and which find a better local minimizer gradually by optimizing the filled function constructed on the minimizer previously found illustrative examples are provided to demonstrate the efficiency and reliability of the proposed filled function method

a computable filled function used for global minimization the filled function method is an approach to find the global minimum of multimodal and multidimensional functions this paper proposes a new filled function this function needs only one parameter and includes neither exponential terms nor logarithmic terms furthermore the lower bound of weight factor a is usually smaller than that of one previous formulation therefore it is reasonable to expect that the proposed function has better computability than the previously reported ones

a new filled function method applied to unconstrained global optimization in this paper we propose a new filled function and give an efficient criterion to choose its two parameters appropriately an algorithm for unconstrained global optimization is developed from this new filled function numerical results with a comparison on many test problems show that this algorithm is efficient and reliable

a class of generalized filled functions with improved computability the filled function method ffm is an approach to find the global minimum of multimodal functions the computability of conventional filled functions is limited as they are defined on either exponential or logarithmic terms this paper proposes a new filled function that does not have such disadvantages numerical experiments on typical testing functions showed that the new function is superior to the conventional one

a statistical view of some chemometrics regression tools chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis in addition to borrowing many techniques from the statistics and engineering literatures chemometrics itself has given rise to several new data analytical methods this article examines two methods commonly used in chemometrics for predictive modeling partial least squares and principal components regression from a statistical perspective the goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations these methods include ordinary least squares variable subset selection and ridge regression

a characterization of binary decision diagrams binary decision diagrams bdds are a representation of boolean functions its use in the synthesis simulation and testing of boolean circuits has been proposed by various researchers in all these applications of bdds solutions to some fundamental computational problems are needed a characterization of bdds in terms of the complexity of these computational problems is presented a tighter bound on the size of an ordered bdd that can be computed from a given boolean circuit is presented on the basis of the results a case is made for exploring the use of repeated bdds with a small number of repeated variables and free bdds for some applications for which only ordered bdds have been used so far

the filled function transformations for constrained global optimization we have found that filled function transformations are very useful in unconstrained global optimization this paper is concerned with constrained global optimization problems and we find several possible ways to find a global solution of such a problem by using a filled function transformation the investigation indicates that using the usual filled function with the original constraints to solve a sequence of constrained local optimization problems is a good approach

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

a new criterion for global robust stability of interval delayed neural networks a novel criterion for the global robust stability of hopfield type interval neural networks with delay is presented an example showing the effectiveness of the present criterion is given

a discrete filled function algorithm embedded with continuous approximation for solving max cut problems in this paper a discrete filled function algorithm embedded with continuous approximation is proposed to solve max cut problems a new discrete filled function is defined for max cut problems and properties of the function are studied in the process of finding an approximation to the global solution of a max cut problem a continuation optimization algorithm is employed to find local solutions of a continuous relaxation of the max cut problem and then global searches are performed by minimizing the proposed filled function unlike general filled function methods characteristics of max cut problems are used the parameters in the proposed filled function need not to be adjusted and are exactly the same for all max cut problems that greatly increases the efficiency of the filled function method numerical results and comparisons on some well known max cut test problems show that the proposed algorithm is efficient to get approximate global solutions of max cut problems

solving nonlinearly constrained global optimization problem via an auxiliary function method this paper considers the nonlinearly constrained continuous global minimization problem based on the idea of the penalty function method an auxiliary function which has approximately the same global minimizers as the original problem is constructed an algorithm is developed to minimize the auxiliary function to find an approximate constrained global minimizer of the constrained global minimization problem the algorithm can escape from the previously converged local minimizers and can converge to an approximate global minimizer of the problem asymptotically with probability one numerical experiments show that it is better than some other well known recent methods for constrained global minimization problems

a new filled function method for nonlinear equations in this paper a new global optimization approach based on the filled function method is proposed for solving box constrained systems of nonlinear equations we first convert the nonlinear system into an equivalent global optimization problem and then propose a new filled function method to solve the converted global optimization problem several numerical examples are presented and solved by using different local minimization methods which illustrate the efficiency of the present approach

test length for pseudorandom testing the process of determining the required test length for a desired level of confidence for pseudorandom testing using a random sampling without replacement model is examined the differences between random and pseudorandom testing are discussed and developed the strictly random testing model is shown to be inaccurate for high confidence testing of combinational circuits a method of calculating the required test length for pseudorandom testing based upon fault detectabilities is described the result provides a very accurate prediction of required test length applicable to self test using pseudorandom inputs

a discrete filled function method for the design of fir filters with signed powers of two coefficients in this paper we consider the optimal design of finite impulse response fir filters with coefficients expressed as sums of signed powers of two spt terms where the normalized peak ripple npr is taken as the performance measure this problem is formulated as a mixed integer programming problem based on a transformation between two different integer spaces and the computation of the optimal scaling factor for a given set of coefficients this mixed integer programming problem is transformed into an equivalent integer programming problem then an efficient algorithm based on a discrete filled function is developed for solving this equivalent problem for illustration some numerical examples are solved

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

the impact of accelerating tools on the interval subdivision algorithm for global optimization abstract the interval subdivision method of moore and skelboe is considered for global optimization the new implementation allows the use of a long list in the procedure which is limited only by the available computer memory standard global optimization test problems are used to measure the efficiency of different versions with or without the monotonicity and the cut off tests of the algorithm the new implementation and the inclusion of the monotonicity test made it possible for the first time for all standard test problems to be solved completely by an interval method moreover in some problems the efficiency of the algorithm was better than that of the best traditional techniques which do not give guaranteed reliability results

the impelling function method applied to global optimization a new global optimization method the impeller function method ifm is proposed in this paper both the theory and the algorithm are presented this new approach is analogous to a classical achievement in the local optimization research the penalty function method pfm therefore the significance of the ifm for global optimization is expected to be similar to that of the pfm for local optimization

a filled function method with one parameter for box constrained global optimization in this paper a new auxiliary function with one parameter on box constrained for escaping the current local minimizer of global optimization problem is proposed first a new definition of the filled function for box constrained minimization problem is given and under mild assumptions this new auxiliary function is really a filled function then a new solution algorithm is proposed according to the theoretical analysis and some numerical results demonstrate the efficiency of this method for box constrained global optimization

global descent method for constrained continuous global optimization abstract in this paper we consider the problem of constrained global optimization of a continuous multivariable function we propose a global descent function technique which requires an easily adjustable single parameter the characteristic property of the proposed function is that each of its local minimizers verifying constraints is a better local minimizer of the objective function or at less an approximated local minimizer with a given tolerance several other properties of the new function are investigated in order to establish a corresponding optimization algorithm we have performed numerical experiments on a set of standard test problems using this algorithm the results illustrate the efficiency of our approach

continuous global optimization through the generation of parametric curves in this paper we develop a new approach for solving a large class of global optimization problems the objective function is only continuous non smooth and non lipschitzian defined on a rectangle of r n this approach is based on the generation in the feasible set of a family of parametrized curves satisfying certain properties combined with the one dimensional evtushenko algorithm to accelerate the corresponding mixed algorithm we have incorporated in a variant a pattern search type deterministic local optimization method and in another variant a new stochastic local optimization method both variants have been applied to several typical test problems a comparison with some well known methods is highlighted through numerical experiments

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

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

global descent method for global optimization this paper develops a novel method the global descent method for solving a general class of global optimization problems this method moves from one local minimizer of the objective function f to a better one at each iteration with the help of an auxiliary function termed the global descent function the global descent function is not only guaranteed to have a local minimizer x over the problem domain in mathbb r n but also ensures that each of its local minimizers is located in some neighborhoods of a better minimizer of f with f x f x these features of the global descent function enable a global descent to be achieved at each iteration using only local descent methods computational experiments conducted on several test problems with up to 1000 variables demonstrate the applicability of the proposed method furthermore numerical comparison experiments carried out with gams baron on several test problems also justify the efficiency and effectiveness of the proposed method

high dimensional robust m estimation asymptotic variance via approximate message passing in a recent article el karoui et al proc natl acad sci 110 36 14557 14562 2013 study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n using numerical simulations and highly plausible heuristic arguments they unveil a striking new phenomenon namely the regression coefficients contain an extra gaussian noise component that is not explained by classical concepts such as the fisher information matrix we show here that that this phenomenon can be characterized rigorously using techniques that were developed by the authors for analyzing the lasso estimator under high dimensional asymptotics we introduce an approximate message passing amp algorithm to compute m estimators and deploy state evolution to evaluate the operating characteristics of amp and so also m estimates our analysis clarifies that the extra gaussian noise encountered in this problem is fundamentally similar to phenomena already studied for regularized least squares in the setting n p

a new discrete filled function algorithm for discrete global optimization a definition of the discrete filled function is given in this paper based on the definition a discrete filled function is proposed theoretical properties of the proposed discrete filled function are investigated and an algorithm for discrete global optimization is developed from the new discrete filled function the implementation of the algorithms on several test problems is reported with satisfactory numerical results

finding discrete global minima with a filled function for integer programming the filled function method is an approach to find the global minimum of multidimensional functions this paper proposes a new definition of the filled function for integer programming problem a filled function which satisfies this definition is presented furthermore we discuss the properties of the filled function and design a new filled function algorithm numerical experiments on several test problems with up to 50 integer variables have demonstrated the applicability and efficiency of the proposed method

on computing signal probability and detection probability of stuck at faults algorithms for the following two problems are presented 1 computing detection probability of stuck at faults cdp and 2 computing signal probability csp these problems arise in the context of random testing pseudorandom testing and testability analysis of combinational circuits the algorithm for cdp combines the notion of supergates and a refinement of th algorithm for cdp presented in the work of s chakravarty and h b hunt iii 1986 the algorithm for cdp can be used to compute the exact value of detection probability of multiple stuck at faults in circuits with multiple outputs single input single output pseudo gates are inserted to model stuck at faults and derive an equivalent single output circuit cdp is thus reduced to the problem of computing the probability distribution of the output over the set of four logic values 0 1d d the algorithm for cdp uses an efficient enumeration algorithm the authors show how the enumeration algorithm can be used to refine the algorithm for csp

a critical review of discrete filled function methods in solving nonlinear discrete optimization problems many real life problems can be modeled as nonlinear discrete optimization problems such problems often have multiple local minima and thus require global optimization methods due to high complexity of these problems heuristic based global optimization techniques are usually required when solving large scale discrete optimization or mixed discrete optimization problems one of the more recent global optimization tools is known as the discrete filled function method nine variations of the discrete filled function method in literature are identified and a review on theoretical properties of each method is given some of the most promising filled functions are tested on various benchmark problems numerical results are given for comparison

a new discrete filled function method for finding global minimizer of the integer programming in this paper a new discrete filled function method is proposed for finding a global minimizer of integer programming problems only one parameter is included in the proposed filled function and it does not need to be adjusted further when it is taken as large as possible moreover the current local minimizer obtained by minimizing the proposed filled function will be one of the local minimizers of the original problem and it is better than the minimizers found previously thus it is not necessary to use a local search method to the original function as a result the computation cost of the proposed discrete filled function method is relatively low numerical results demonstrate the effectiveness of the proposed method

a one parameter filled function method applied to nonsmooth constrained global optimization in this paper we propose a filled function method for solving nonsmooth constrained global optimization problems based on a new definition of the filled function a more practical one parameter filled function is constructed which overcomes some drawbacks of the previous filled functions then a corresponding algorithm is presented it attains a local minimizer by implementing a local search procedure and finds a better local minimizer gradually by optimizing the filled function constructed on the minimizer previously found by repeating these steps a global minimizer is obtained numerical experiments are presented to show the practicability of the proposed filled function method in the end extension conceivable applications are given in order to evaluate the merits of this method

a new filled function method for constrained nonlinear equations abstract in this paper we extend the filled function method proposed in lin et al 2009 10 to solve the constrained system of nonlinear equations and we propose two methods to find a solution of such a system finally the efficiency of the present method is illustrated through some examples

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

coefficient estimation of iir filter by a multiple crossover genetic algorithm this paper proposes an improved genetic algorithm ga with multiple crossovers to estimate the system coefficients for the infinite impulse response iir digital filter in the traditional crossover operation it needs two parent chromosomes to achieve the crossover work whereas in this paper the proposed algorithm selects three chromosomes for crossover in order to generate more promising offspring toward the problem solution each of unknown iir coefficients is called a gene and the collection of genes forms a chromosome a population of chromosomes is evolved by the genetic operations of reproduction multiple crossover and mutation finally two illustrative examples including the band pass and band stop iir filters are demonstrated to verify the proposed method

a cut peak function method for global optimization a new method is proposed for solving box constrained global optimization problems the basic idea of the method is described as follows constructing a so called cut peak function and a choice function for each present minimizer the original problem of finding a global solution is converted into an auxiliary minimization problem of finding local minimizers of the choice function whose objective function values are smaller than the previous ones for a local minimum solution of auxiliary problems this procedure is repeated until no new minimizer with a smaller objective function value could be found for the last minimizer construction of auxiliary problems and choice of parameters are relatively simple so the algorithm is relatively easy to implement and the results of the numerical tests are satisfactory compared to other methods

a continuous approach to nonlinear integer programming this paper is concerned with nonlinear integer programming problems unconstrained and constrained as well as mixed the problems are transformed into nonlinear global optimization problems and then solved by the filled function transformation method this approach should be efficient since it has been shown that the filled function transformation method is efficient in solving global optimization problems with large numbers up to 30 2 5 in the present examples of local minimizers however the sense of efficient as having polynomial complexity in the worst or average case is not suitable for nonlinear integer programming problems since the complexity of a nonlinear programming algorithm is in general nonpolynomial

a new filled function method for unconstrained global optimization in this paper a new definition of the filled function is given it is different from the primary definition which was given by ge in paper r p ge a filled function method for finding a global minimzer of a function of several variables math program 46 1990 191 204 based on the definition a new filled function is proposed and it has better properties an algorithm for unconstrained global optimization is developed from the new filled function the implementation of the algorithm on several test problems is reported with satisfactory numerical results

a filled function method for minimizing control variation in constrained discrete time optimal control problems abstract this paper considers a discrete time optimal control problem subject to terminal state constraints and all time step inequality constraints where the cost function involves a terminal cost a summation cost and a penalty on the change of the control action the variation of the control signal and the all time step constraints are non smooth functions thus this optimal control problem is formulated as a non smooth constrained optimization problem however it is nonconvex and hence it may have many local minimum points thus a filled function method is introduced in conjunction with local optimization techniques to solve this non smooth and nonconvex constrained optimization problem for illustration two numerical examples are presented and solved using the proposed approach

a discrete filled function algorithm for approximate global solutions of max cut problems a discrete filled function algorithm is proposed for approximate global solutions of max cut problems a new discrete filled function is defined for max cut problems and the properties of the filled function are studied unlike general filled function methods using the characteristic of max cut problems the parameters in proposed filled function need not be adjusted this greatly increases the efficiency of the filled function method by combining a procedure that randomly generates initial points for minimization of the filled function the proposed algorithm can greatly reduce the calculation cost and be applied to large scale max cut problems numerical results on different sizes and densities test problems indicate that the proposed algorithm is efficient and stable to get approximate global solutions of max cut problems

a new filled function algorithm for constrained global optimization problems a new filled function with one parameter is proposed for solving constrained global optimization problems without the coercive condition in which the filled function contains neither exponential term nor fractional term and is easy to be calculated a corresponding filled function algorithm is established based on analysis of the properties of the filled function at last we perform numerical experiments on some typical test problems using the algorithm and the detailed numerical results show that the algorithm is effective

stability analysis for the generalized cohen grossberg neural networks with inverse lipschitz neuron activations in this paper by using nonsmooth analysis approach linear matrix inequality lmi technique topological degree theory and lyapunov krasovskii function method the issue of global exponential stability is investigated for a class of generalized cohen grossberg neural networks possessing inverse lipschitz neuron activations and nonsmooth behaved functions several novel delay dependent sufficient conditions are established towards the existence uniqueness and global exponential stability of the equilibrium point which are shown in terms of lmis it is noted that the results above require neither the lipschitz continuity of the activation functions nor the smoothness of the behaved functions also for the case of the activation function that satisfies not only the inverse lipschitz conditions but also the lipschitz conditions some conditions are derived which generalize the previous results finally two examples with their simulations are given to show the effectiveness of the theoretical results

high dimensional variable selection this paper explores the following question what kind of statistical guarantees can be given when doing variable selection in high dimensional models in particular we look at the error rates and power of some multi stage regression methods in the first stage we fit a set of candidate models in the second stage we select one model by cross validation in the third stage we use hypothesis testing to eliminate some variables we refer to the first two stages as screening and the last stage as cleaning we consider three screening methods the lasso marginal regression and forward stepwise regression our method gives consistent variable selection under certain conditions

revised filled function methods for global optimization this paper considers the unconstrained global optimization with the revised filled function methods the minimization sequence could leave from a local minimizer to a better minimizer of the objective function through solving an unary equation or minimizing an auxiliary function constructed at the local minimizer some promising numerical results are also included

an approximate algorithm for nonlinear integer programming this paper presents an approximate algorithm which is modified from the filled function method for continuous global optimization to solve nonlinear integer programming problems unlike the other approximate methods the algorithm tries to improve a discrete local minimal solution by minimizing a filled function it is a direct method numerical experiments show that this algorithm is efficient

a new class of filled functions with one parameter for global optimization the filled function method is an efficient approach for finding global minimizers of multi dimensional and nonlinear functions in the absence of any restrictions in this paper we give a new definition of filled function and the idea of constructing a new filled function and then a new class of filled functions with one parameter on the basis of the new definition which possesses better quality is presented theoretical properties of the new class of filled functions are investigated a new algorithm is developed from the new filled function method the implementation of the algorithm on seven test problems with dimensions up to 30 is reported and comparisons with other filled function methods demonstrate that the new algorithm is more efficient

a parallel computing scheme for minimizing a class of large scale functions this paper gives a parallel computing scheme for minimizing a twice continuously differentiable function with the form f x i email protected i x i i email protected j 1 j i m i j x i x j where x x t 1 x t m t and x i r n i m i 1n i n and n a very big number it is proved that we may use m parallel processors and an iterative procedure to find a minimizer of x the convergence and convergence rate are given under some conditions the conditions for finding a global minimizer of x by using this scheme are given too a similar scheme can also be used parallelly to solve a large scale system of nonlinear equations in the similar way a more general case is also investigated

two new classes of filled functions the filled function method is an effective approach to find the global minimizer two of the recently proposed filled functions are l x and l 2 x having observed that the second term in l x or l 2 x may result in undesirable computational behaviors in this paper we propose a new function l 3 x having also realized that the essence of the mitigation is to eliminate the discontinuity we propose another new function l 4 x both theoretical analysis and numerical testing results are presented

high dimensionality effects in the markowitz problem and other quadratic programs with linear constraints risk underestimation we study the properties of solutions of quadratic programs with linear equality constraints whose parameters are estimated from data in the high dimensional setting where p the number of variables in the problem is of the same order of magnitude as n the number of observations used to estimate the parameters the markowitz problem in finance is a subcase of our study assuming normality and independence of the observations we relate the ecient frontier computed empirically to the true ecient frontier our computations show that there is a separation of the errors induced by estimating the mean of the observations and estimating the covariance matrix in particular the price paid for estimating the covariance matrix is an underestimation of the variance by a factor roughly equal to 1 p n therefore the risk of the optimal population solution is underestimated when we estimate it by solving a similar quadratic program with estimated parameters we also characterize the statistical behavior of linear functionals of the empirical optimal vector and show that they are biased estimators of the corresponding population quantities we investigate the robustness of our gaussian results by extending the study to certain elliptical models and models where our n observations are correlated in time we show a lack of robustness of the gaussian results but are still able to get results concerning rst order properties of the quantities of interest even in the case of relatively heavy tailed data we require two moments risk underestimation is still present in the elliptical case and more pronounced that in the gaussian case we discuss properties of the non parametric and parametric bootstrap in this context we show several results including the interesting fact that standard applications of the bootstrap generally yields inconsistent estimates of bias finally we propose some strategies to correct these problems and practically validate them in some simulations in all the paper we will assume that p n and n p tend to innity and p n

asymptotic properties of bridge estimators in sparse high dimensional regression models we study the asymptotic properties of bridge estimators in sparse high dimensional linear regression models when the number of covariates may increase to infinity with the sample size we are particularly interested in the use of bridge estimators to distinguish between covariates whose coefficients are zero and covariates whose coefficients are nonzero we show that under appropriate conditions bridge estimators correctly select covariates with nonzero coefficients with probability converging to one and that the estimators of nonzero coefficients have the same asymptotic distribution that they would have if the zero coefficients were known in advance thus bridge estimators have an oracle property in the sense of fan and li j amer statist assoc 96 2001 1348 1360 and fan and peng ann statist 32 2004 928 961 in general the oracle property holds only if the number of covariates is smaller than the sample size however under a partial orthogonality condition in which the covariates of the zero coefficients are uncorrelated or weakly correlated with the covariates of nonzero coefficients we show that marginal bridge estimators can correctly distinguish between covariates with nonzero and zero coefficients with probability converging to one even when the number of covariates is greater than the sample size