convergence rates for forward backward dynamical systems associated with strongly monotone inclusions abstract we investigate the convergence rates of the trajectories generated by implicit first and second order dynamical systems associated to the determination of the zeros of the sum of a maximally monotone operator and a monotone and lipschitz continuous one in a real hilbert space we show that these trajectories strongly converge with exponential rate to a zero of the sum provided the latter is strongly monotone we derive from here convergence rates for the trajectories generated by dynamical systems associated to the minimization of the sum of a proper convex and lower semicontinuous function with a smooth convex one provided the objective function fulfills a strong convexity assumption in the particular case of minimizing a smooth and strongly convex function we prove that its values converge along the trajectory to its minimum value with exponential rate too

adaptive configuration of evolutionary algorithms for constrained optimization in the literature many different evolutionary algorithms eas with different search operators have been reported for solving optimization problems however no single algorithm is consistently able to solve all types of problems to overcome this problem the recent trend is to use a mix of operators within a single algorithm there are also cases where multiple methodologies each with a single search operator have been used under one approach these approaches outperformed the single operator based single algorithm approaches in this paper we propose a new algorithm framework that uses multiple methodologies where each methodology uses multiple search operators we introduce it as the ea with adaptive configuration where the first level is to decide the methodologies and the second level is to decide the search operators in this approach all operators and population sizes are updated adaptively although the framework may sound complex one can gain significant benefits from it in solving optimization problems the proposed framework has been tested by solving two sets of specialized benchmark problems the results showed a competitive if not better performance when it was compared to the state of the art algorithms moreover the proposed algorithm significantly reduces the computational time in comparison to both single and multi operator based algorithms

ensemble of differential evolution variants abstract differential evolution de is one of the most popular and efficient evolutionary algorithms for numerical optimization and it has gained much success in a series of academic benchmark competitions as well as real applications recently ensemble methods receive an increasing attention in designing high quality de algorithms however previous efforts are mainly devoted to the low level ensemble of mutation strategies of de this study investigates the high level ensemble of multiple existing efficient de variants a multi population based framework mpf is proposed to realize the ensemble of multiple de v ariants to derive a new algorithm named edev for short edev consists of three highly popular and efficient de variants namely jade adaptive differential evolution with optional external archive code differential evolution with composite trial vector generation strategies and control parameters and epsde differential evolution algorithm with ensemble of parameters and mutation strategies the whole population of edev is partitioned into four subpopulations including three indicator subpopulations with smaller size and one reward subpopulation with much larger size each constituent de variant in edev owns an indicator subpopulation after every predefined generations the most efficient constituent de variant is determined and the reward subpopulation is assigned to that best performed de variant as an extra reward through this manner the most efficient de variant is expected to obtain the most computational resources during the optimization process in addition the population partition operator is triggered at every generation which results in timely information sharing and tight cooperation among the component de variants extensive experiments and comparisons have been done based on the cec2005 and cec2014 benchmark suit which shows that the overall performance of edev is superior to several state of the art peer de variants the success of edev reveals that through an appropriate ensemble framework different de variants of different merits can support one another to cooperatively solve optimization problems

infinite dimensional features of matrices and pseudospectra abstract given a hilbert space operator t the level sets of function t z t z 1 1 determine the so called pseudospectra of t we set t to be zero on the spectrum of t after giving some elementary properties of t which as it seems were not noticed before we apply them to the study of the approximation we prove that for any operator t there is a sequence t n of finite matrices such that t n z tends to t z uniformly on c in this proof quasitriangular operators play a special role this is merely an existence result we do not give a concrete construction of this sequence of matrices one of our main points is to show how to use infinite dimensional operator models in order to produce examples and counterexamples in the set of finite matrices of large size in particular we get a result which means in a sense that the pseudospectrum of a nilpotent matrix can be anything one can imagine we also study the norms of the multipliers in the context of cowen douglas class operators we use these results to show that to the opposite to the function s the function s z for certain finite matrices s may oscillate arbitrarily fast even far away from the spectrum

prox penalization and splitting methods for constrained variational problems this paper is concerned with the study of a class of prox penalization methods for solving variational inequalities of the form ax n c x ni0 where mathcal h is a real hilbert space a mathcal h rightrightarrows mathcal h is a maximal monotone operator and n c is the outward normal cone to a closed convex set c subset mathcal h given psi mathcal h to mathbb r cup infty which acts as a penalization function with respect to the constraint x in c and a penalization parameter beta n we consider a diagonal proximal algorithm of the form x n i lambda n a beta n partial psi 1 x n 1 and an algorithm which alternates proximal steps with respect to a and penalization steps with respect to c and reads as x n i lambda n beta n partial psi 1 i lambda na 1 x n 1 we obtain weak ergodic convergence for a general maximal monotone operator a and weak convergence of the whole sequence x n when a is the subdifferential of a proper lower semicontinuous convex function mixing with passty s idea we can extend the ergodic convergence theorem thus obtaining the convergence of a prox penalization splitting algorithm for constrained variational inequalities governed by the sum of several maximal monotone operators our results are applied to an optimal control problem where the state variable and the control are coupled by an elliptic equation we also establish robustness and stability results that account for numerical approximation errors

evolutionary programming using a mixed mutation strategy abstract different mutation operators have been proposed in evolutionary programming but for each operator there are some types of optimization problems that cannot be solved efficiently a mixed strategy integrating several mutation operators into a single algorithm can overcome this problem inspired by evolutionary game theory this paper presents a mixed strategy evolutionary programming algorithm that employs the gaussian cauchy levy and single point mutation operators the novel algorithm is tested on a set of 22 benchmark problems the results show that the mixed strategy performs equally well or better than the best of the four pure strategies does for all of the benchmark problems

asymptotic control and stabilization of nonlinear oscillators with non isolated equilibria let h r be a c1 function on a real hilbert space h and let 0 be a positive damping parameter for any control function e r r which tends to zero as t we study the asymptotic behavior of the trajectories of the damped nonlinear oscillator hbfc x t x t x t e t x t 0 we show that if e t does not tend to zero too rapidly as t then the term e t x t asymptotically acts as a tikhonov regularization which forces the trajectories to converge to a particular equilibrium indeed in the main result of this paper it is established that when is convex and s argmin under the key assumption that e is a slow control i e 0 e t dt then each trajectory of the hbfc system strongly converges as t to the element of minimal norm of the closed convex set s as an application we consider the damped wave equation with neumann boundary condition formula

cluster based population initialization for differential evolution frameworks this article proposes a procedure to perform an intelligent initialization for population based algorithms the proposed pre processing procedure namely cluster based population initialization cbpi consists of three consecutive stages at the first stage the individuals belonging to a randomly sampled population undergo two subsequent local search algorithms i e a simple local search that performs moves along the axes and rosenbrock algorithm at the second stage the solutions processed by the two local searches undergo the k means clustering algorithm and are grouped into sets on the basis of their euclidean distance at the third stage the best individuals belonging to each cluster are saved into the initial population of a generic optimization algorithm if the population has not been yet filled the other individuals of the population are sampled within the clusters by using a fitness based probabilistic criterion this three stage procedure implicitly performs an initial screening of the problem features in order to roughly estimate the most interesting regions of the decision space the proposed cbpi has been tested on multiple classical and modern differential evolution variants on a wide array of test problems and dimensionality values as well as on a real world problem the proposed intelligent sampling appears to have a significant impact on the algorithmic functioning as it consistently enhances the performance of the algorithms with which it is integrated

modified cuckoo search algorithm with self adaptive parameter method the cuckoo search algorithm cs is a simple and effective global optimization algorithm it has been applied to solve a wide range of real world optimization problem in this paper the proposed method uses two new mutation rules based on the rand and best individuals among the entire population in order to balance the exploitation and exploration of the algorithm the new rules are combined through a linear decreasing probability rule then self adaptive parameter setting is introduced as a uniform random value to enhance the diversity of the population based on the relative success number of the proposed two new parameters in the previous period to verify the performance of sacs 16 benchmark functions chosen from literature are employed experimental results indicate that the proposed method performs better than or at least comparable to state of the art methods from literature when considering the quality of the solutions obtained in the last part experiments have been conducted on lorenz system and chen system to estimate the parameters of these two chaotic systems simulation results further demonstrate the proposed method is very effective

proximal point algorithm controlled by a slowly vanishing term applications to hierarchical minimization let phi 0 mathbb r n to mathbb r cup infty be a closed convex function and phi 1 mathbb r n to mathbb r be a finite convex function that are bounded from below our goal is to build an algorithm which first minimizes the map phi 0 and secondly the map phi 1 over the set s 0 rm argmin phi 0 for that purpose we define the following proximal type algorithm x n 1 x n lambda n in partial eta n phi 0 varepsilon n phi 1 x n 1 leqno mathcal a 1 where lambda n is a positive step sequence eta n is a summable error sequence and varepsilon n is a control sequence tending toward 0 partial eta denotes the eta approximate subdifferential when varepsilon n is a slow control i e sum n 0 infty varepsilon n infty we prove that under adequate conditions the sequence x n defined by mathcal a 1 tends toward an element of s 1 rm argmin s 0 phi 1 more generally given finite convex functions phi 2 ldots phi n mathbb r n to mathbb r let us define the sets s i i in 1 ldots n by the recursive relation s i rm argmin s i 1 phi i we introduce an extension of algorithm mathcal a 1 to minimize hierarchically each function phi i on the set s i 1 for i in 1 ldots n

strong asymptotic convergence of evolution equations governed by maximal monotone operators with tikhonov regularization abstract we consider the tikhonov like dynamics u t a u t e t u t where a is a maximal monotone operator on a hilbert space and the parameter function e t tends to 0 as t with 0 e t d t when a is the subdifferential of a closed proper convex function f we establish strong convergence of u t towards the least norm minimizer of f in the general case we prove strong convergence towards the least norm point in a 1 0 provided that the function e t has bounded variation and provide a counterexample when this property fails

asymptotic behavior of coupled dynamical systems with multiscale aspects abstract we study the asymptotic behavior as time variable t goes to of nonautonomous dynamical systems involving multiscale features as a benchmark case given h a general hilbert space h r and h r two closed convex functions and a function of t which tends to as t goes to we consider the differential inclusion x t x t t x t 0 this system models the emergence of various collective behaviors in game theory as well as the asymptotic control of coupled systems we show several results ranging from weak ergodic to strong convergence of the trajectories as a key ingredient we assume that for every p belonging to the range of n c 0 t p t c p t d t where is the fenchel conjugate of c is the support function of c argmin and n c x is the normal cone to c at x as a by product we revisit the system x t t x t x t 0 where t tends to zero as t goes to and 0 t d t whose asymptotic behavior can be derived from the preceding one by time rescaling applications are given in game theory optimal control variational problems and pdes

asymptotic behavior of solutions to a class of nonlinear evolution equations on etudie les equations de la chaleur a controle de temperature a l interieur ou sur la frontiere du domaine pour cela on considere un type de problemes variationnels paraboliques avec obstacles

estimates for the spectrum near algebraic elements abstract we extend a result of s friedland linear algebra appl 12 1982 81 98 on the variation of eigenvalues of matrices to show that if a b are elements of a banach algebra both algebraic of degree at most n then the hausdorff distance between their spectra satisfies a b n c n 2m n 1 a b where m max a b and c n 23n 13 the same technique also re proves a local form of this result obtained earlier by b aupetit and j zemanek linear algebra appl 52 53 1983 39 44 but with improved bounds on the constants we further investigate the sharpness of these bounds

epistatic arithmetic crossover based on cartesian graph product in ensemble differential evolution epistasis in genetics denotes an impact of one gene on the expression of the another genes this means that so called epistatic gene influences the characteristics of the so called hypostatic genes as a matter of fact there is no one to one correspondence between genes and traits in nature on the other hand values of offspring genes are inherited from the parents genes in this paper the impact of epistatic genes in evolutionary computation is studied where each epistatic gene in offspring depends on the corresponding hypostatic genes of its parents by an epistatic arithmetic crossover used in differential evolution thus epistatic genes are determined by the cartesian graph product of both parents presented as linear graphs the epistatic arithmetic crossover is applied as a mutation strategy to the ensemble differential evolution the results of extensive experiments conducted on cec 14 function benchmark suite showed a great potential of the proposed algorithm and encouraged us to start to experiment with other graph products as well

weak convergence of a relaxed and inertial hybrid projection proximal point algorithm for maximal monotone operators in hilbert space this paper introduces a general implicit iterative method for finding zeros of a maximal monotone operator in a hilbert space which unifies three previously studied strategies relaxation inertial type extrapolation and projection step the first two strategies are intended to speed up the convergence of the standard proximal point algorithm while the third permits one to perform inexact proximal iterations with fixed relative error tolerance the paper establishes the global convergence of the method for the weak topology under appropriate assumptions on the algorithm parameters

a new class of alternating proximal minimization algorithms with costs to move given two objective functions f mathcal x mapsto r cup infty and g mathcal y mapsto r cup infty on abstract spaces mathcal x and mathcal y and a coupling function c mathcal x times mathcal y mapsto r we introduce and study alternative minimization algorithms of the following type x 0 y 0 in mathcal x times mathcal y mbox given x n y n rightarrow x n 1 y n rightarrow x n 1 y n 1 mbox as follows left begin array l x n 1 in mbox argmin f xi beta n c xi y n alpha n h x n xi xi in mathcal x y n 1 in mbox argmin g eta mu n c x n 1 eta nu n k y n eta eta in mathcal y end array right their most original feature is the introduction of the terms h mathcal x times mathcal x mapsto r and k mathcal y times mathcal y mapsto r which are costs to change or to move distance like functions relative entropies accounting for various inertial friction or anchoring effects these algorithms are studied in a general abstract framework the introduction of the costs to change h and k leads to proximal minimizations with corresponding dissipative effects as a result the algorithms enjoy nice convergent properties coefficients alpha n beta n mu n nu n are nonnegative parameters when taking alpha n nu n 0 and quadratic costs on a hilbert space one recovers the classical alternating minimization algorithm which itself is a natural extension of the alternating projection algorithm of von neumann a number of new significant results hold in general metric spaces we pay particular attention to the following cases 1 mathcal x d mathcal x and mathcal y d mathcal y are complete metric spaces and h geq d mathcal x k geq d mathcal y high local costs to move the algorithms then provide sequences that converge to nash equilibria 2 mathcal x mathcal y mathcal h is a hilbert space the costs to change are quadratic low local costs to move and the functions f g mathcal h mapsto r cup infty are closed convex proper then some of the classical convergence theorems for alternating convex minimization algorithms including those of acker and prestel are properly extended with original proofs

asymptotic control and stabilization of nonlinear oscillators with non isolated equilibria a note from l 1 to non l 1 in h attouch m o czarnecki asymptotic control and stabilization of non linear oscillators with non isolated equilibria j differential equations 179 2002 278 310 we exhibited a sharp condition ensuring the efficiency of the tikhonov like control term in the hbfc system precisely let h r be a c1 function on a real hilbert space h let 0 be a positive damping parameter and let r r be a control function which decreases to zero as t in order to select particular equilibria in the important case where has non isolated equilibria we introduced in h attouch m o czarnecki j differential equations 179 2002 278 310 the following damped nonlinear oscillator and studied its asymptotic behavior hbfc x t x t x t t x t 0 we established that when is convex and s argmin under the key assumption that is a slow control i e 0 t dt then each trajectory of the hbfc system strongly converges when t to the element of minimal norm of the closed convex set s the condition on the control term is sharp indeed when 0 t dt the trajectory weakly converges but it may not strongly converge and we have no information a priori on the weak limit in this note we give an answer to the following question when does an l1 control term becomes or behave non l1 precisely take a control term l1 let x be the solution of the corresponding hbfc system take n to be a non increasing truncation of n t t for t 0 n let x be the solution of the corresponding hbfc system we show that limn xn x 0 in particular the weak limits of the trajectories xn strongly converge when n to the strong limit of the trajectory x in other words there is no loss of the information gained by the slow behavior for t n

optimal depth estimation by combining focus measures using genetic programming three dimensional 3d shape reconstruction is a fundamental problem in machine vision applications shape from focus sff is one of the passive optical methods for 3d shape recovery that uses degree of focus as a cue to estimate 3d shape in this approach usually a single focus measure operator is applied to measure the focus quality of each pixel in the image sequence however the applicability of a single focus measure is limited to estimate accurately the depth map for diverse type of real objects to address this problem we develop optimal composite depth ocd function through genetic programming gp for accurate depth estimation the ocd function is constructed by optimally combining the primary information extracted using one or more focus measures the genetically developed composite function is then used to compute the optimal depth map of objects the performance of the developed nonlinear function is investigated using both the synthetic and the real world image sequences experimental results demonstrate that the proposed estimator is more useful in computing accurate depth maps as compared to the existing sff methods moreover it is found that the heterogeneous function is more effective than homogeneous function

asymptotic behavior of nonautonomous monotone and subgradient evolution equations in a hilbert setting h we study the asymptotic behavior of the trajectories of nonautonomous evolution equations dot x t a t x t ni 0 where for each t geq 0 a t h rightrightarrows h denotes a maximal monotone operator we provide general conditions guaranteeing the weak ergodic convergence of each trajectory x cdot to a zero of a limit maximal monotone operator a infty as the time variable t tends to infty the crucial point is to use the brezis haraux function or equivalently the fitzpatrick function to express at which rate the excess of mathrm gph a infty over mathrm gph a t tends to zero this approach gives a sharp and unifying view of this subject in the case of operators a t partial phi t which are subdifferentials of proper closed convex functions phi t we show convergence results for the trajectories then we specialize our results to multiscale evolution equations and obtain asymptotic properties of hierarchical minimization and selection of viscosity solutions illustrations are given in the field of coupled systems and partial differential equations

explicit upper bounds for the spectral distance of two trace class operators abstract given two trace class operators a and b on a separable hilbert space we provide an upper bound for the hausdorff distance of their spectra involving only the distance of a and b in operator norm and the singular values of a and b by specifying particular asymptotics of the singular values our bound reproduces or improves existing bounds for the spectral distance the proof is based on lower and upper bounds for determinants of trace class operators of independent interest

ensemble strategies with adaptive evolutionary programming mutation operators such as gaussian levy and cauchy have been used with evolutionary programming ep according to the no free lunch theorem it is impossible for ep with a single mutation operator to outperform always for example classical ep cep with gaussian mutation is better at searching in a local neighborhood while the fast ep fep with the cauchy mutation performs better over a larger neighborhood motivated by these observations we propose an ensemble approach where each mutation operator has its associated population and every population benefits from every function call this approach enables us to benefit from different mutation operators with different parameter values whenever they are effective during different stages of the search process in addition the recently proposed adaptive ep aep using gaussian acep and cauchy afep mutations is also evaluated in the aep the strategy parameter values are adapted based on the search performance in the previous few generations the performance of ensemble is compared with a mixed mutation strategy which integrates several mutation operators into a single algorithm as well as against the aep with a single mutation operator improved performance of the ensemble over the single mutation based algorithms and mixed mutation algorithm is verified using statistical tests

approaching the solving of constrained variational inequalities via penalty term based dynamical systems abstract we investigate the existence and uniqueness of locally absolutely continuous trajectories of a penalty term based dynamical system associated to a constrained variational inequality expressed as a monotone inclusion problem relying on lyapunov analysis and on the ergodic continuous version of the celebrated opial lemma we prove weak ergodic convergence of the orbits to a solution of the constrained variational inequality under investigation if one of the operators involved satisfies stronger monotonicity properties then strong convergence of the trajectories can be shown

counterexample to a conjecture of elsner on the spectral variation of matrices abstract in 1985 elsner proved that the hausdorff distance between the spectra of two n n matrices a and b satisfies a b n a b n 1 a b where denotes the operator norm with respect to the euclidean norm on c n he further conjectured that the same inequality holds for all operator norms we disprove this conjecture and also the weaker conjecture where a b is replaced by 2max a b

asymptotic behaviour of quasi autonomous dissipative systems in hilbert spaces abstract by suitably modifying the methods used by b djafari rouhani ergodic theorems for non expansive sequences in hilbert spaces and related problems part i pp 1 76 thesis yale university and a new proof of the weak convergence theorems for non expansive sequences and curves in hilbert spaces preprint 1984 and by b djafari rouhani and s kakutani ergodic theorems for non expansive non linear operators in a hilbert space preprint 1984 we study the asymptotic behaviour of the quasi autonomous dissipative system du dt au where a is a monotone operator in a hilbert space h and l 1 0 h

multicriteria fuzzy control using evolutionary programming abstract in this paper we propose a multicriteria fuzzy control mfc using evolutionary programming ep by which its fuzzy measure is optimized basically the mfc is an extended version of the existing fuzzy logic controller to obtain the proper weights of the fuzzy rules for the fine tuning control the mfc is designed by three steps first the attributes of the system output response are selected second the partial evaluations from the viewpoints of the attributes are assigned to the fuzzy rules and third the fuzzy integral is employed to aggregate the partial evaluation and the user s fuzzy measure about the consideration degree of each attribute for the proper weight value ep is used to optimize the fuzzy measure for the linear tuning property of the mfc computer simulations indicate that the proposed scheme has excellent performance

penalization in non classical convex programming via variational convergence a penalty method for convex functions which cannot necessarily be extended outside their effective domains by an everywhere finite convex function is proposed and combined with the proximal method proofs of convergence rely on variational convergence theory

a comparative study of variation operators used for evolutionary multi objective optimization abstract in this paper several variation operators based on pareto efficiency extracted from differential evolution estimation of distribution algorithms evolution strategies and evolutionary programming are compared in order to determine whether or not they increase the performance of the non pareto based versions firstly we compare the selected variation operators in pairs each operator with a modification of itself in which we remove those elements related to the pareto efficiency then in a second experiment we compare among the selected operators the variation operators used in the nsga ii algorithm and the ones presented by the authors pbco and rbmo in all the experiments the variation operators are incorporated in a well known algorithm usually considered as a reference for making the comparisons the nsga ii algorithm the experiments show that the pareto based variation operators selected from the literature do not usually present a better behavior than their non pareto based versions and none of them presents a better performance than the one reached by the variation operators defined by the authors which were entirely built around the pareto information of the individuals these facts suggest that more effort should be placed in the design of variation operators devoted to multi objective algorithms in order to achieve superior results to those obtained by means of general variation operators

explicit eigenvalue estimates for transfer operators acting on spaces of holomorphic functions abstract we consider transfer operators acting on spaces of holomorphic functions and provide explicit bounds for their eigenvalues more precisely if is any open set in c d and l is a suitable transfer operator acting on bergman space a 2 its eigenvalue sequence n l is bounded by n l a exp a n 1 d where a a 0 are explicitly given

alternating proximal algorithms for linearly constrained variational inequalities application to domain decomposition for pde s abstract let x y z be real hilbert spaces let f x r g y r be closed convex functions and let a x z b y z be linear continuous operators let us consider the constrained minimization problem p min f x g y a x b y given a sequence n which tends toward 0 as n we study the following alternating proximal algorithm a x n 1 argmin n 1 f 1 2 a b y n z 2 2 x n x 2 x y n 1 argmin n 1 g 1 2 a x n 1 b z 2 2 y n y 2 y where and are positive parameters it is shown that if the sequence n tends moderately slowly toward 0 then the iterates of a weakly converge toward a solution of p the study is extended to the setting of maximal monotone operators for which a general ergodic convergence result is obtained applications are given in the area of domain decomposition for pde s

stabilization of oscillators subject to dry friction finite time convergence versus exponential decay results we investigate the dynamics of an oscillator subject to dry friction via the following differential inclusion s x t x t f x t 0 t 0 where f r n r is a smooth potential and r n r is a convex function the friction is modelized by the subdifferential term x when 0 int 0 dry friction condition it was shown by adly attouch and cabot 2006 that the unique solution to s converges in a finite time toward an equilibrium state too provided that f x int 0 in this paper we study the delicate case where the vector f x belongs to the boundary of the set 0 we prove that either the solution converges in a finite time or the speed of convergence is exponential when a b 2 2 a 0 b 0 we obtain the existence of a critical coefficient be 0 below which every solution stabilizes in a finite time it is also shown that the geometry of the set 0 plays a central role in the analysis

convergence of a relaxed inertial proximal algorithm for maximally monotone operators in a hilbert space mathcal h given a mathcal h rightarrow 2 mathcal h a maximally monotone operator we study the convergence properties of a general class of relaxed inertial proximal algorithms this study aims to extend to the case of the general monotone inclusion ax ni 0 the acceleration techniques initially introduced by nesterov in the case of convex minimization the relaxed form of the proximal algorithms plays a central role it comes naturally with the regularization of the operator a by its yosida approximation with a variable parameter a technique recently introduced by attouch peypouquet math program ser b 2018 https doi org 10 1007 s10107 018 1252 x for a particular class of inertial proximal algorithms our study provides an algorithmic version of the convergence results obtained by attouch cabot j differ equ 264 7138 7182 2018 in the case of continuous dynamical systems

a convergence result for nonautonomous subgradient evolution equations and its application to the steepest descent exponential penalty trajectory in linear programming abstract we present a new result on the asymptotic behavior of nonautonomous subgradient evolution equations of the form u t t u t where t t 0 is a family of closed proper convex functions the result is used to study the flow generated by the family t x f x r t where f x r ctx r exp aix bi r is the exponential penalty approximation of the linear program min ctx ax b and r t is a positive function tending to 0 when t we prove that the trajectory u t converges to an optimal solution u of the linear program and we give conditions for the convergence of an associated dual trajectory t toward an optimal solution of the dual program

an optimal bound for the spectral variation of two matrices abstract we establish a bound for the spectral variation of two complex n n matrices a b in terms of a b and a b here denotes the spectral norm it is always better than a bound previously given by bhatia and friedland and it is optimal we describe the set of pairs a b for which the bound is attained

asymptotic behavior of gradient like dynamical systems involving inertia and multiscale aspects abstract in a hilbert space h we study the asymptotic behavior as time variable t goes to of nonautonomous gradient like dynamical systems involving inertia and multiscale features given h r and h r two convex differentiable functions a positive damping parameter and t a function of t which tends to zero as t goes to we consider the second order differential equation x t x t x t t x t 0 this system models the emergence of various collective behaviors in game theory as well as the asymptotic control of coupled nonlinear oscillators assuming that t tends to zero moderately slowly as t goes to infinity we show that the trajectories converge weakly in h the limiting equilibria are solutions of the hierarchical minimization problem which consists in minimizing over the set c of minimizers of as key assumptions we suppose that 0 t d t and that for every p belonging to a convex cone c depending on the data and 0 t p c t p d t where is the fenchel conjugate of and c is the support function of c an application is given to coupled oscillators

ensemble of niching algorithms although niching algorithms have been investigated for almost four decades as effective procedures to obtain several good and diverse solutions of an optimization problem no effort has been reported on combining different niching algorithms to form an effective ensemble of niching algorithms in this paper we propose an ensemble of niching algorithms ena and illustrate the concept by an instantiation which is realized using four different parallel populations the offspring of each population is considered by all parallel populations the instantiation is tested on a set of 16 real and binary problems and compared against the single niching methods with respect to searching ability and computation time results confirm that ena method is as good as or better than the best single method in it on every test problem moreover comparison with other state of the art niching algorithms demonstrates the competitiveness of our proposed ena

eigenclassifiers for combining correlated classifiers in practice classifiers in an ensemble are not independent this paper is the continuation of our previous work on ensemble subset selection a ulas m semerci o t yildiz e alpaydin incremental construction of classifier and discriminant ensembles information sciences 179 9 2009 1298 1318 and has two parts first we investigate the effect of four factors on correlation i algorithms used for training ii hyperparameters of the algorithms iii resampled training sets iv input feature subsets simulations using 14 classifiers on 38 data sets indicate that hyperparameters and overlapping training sets have higher effect on positive correlation than features and algorithms second we propose postprocessing before fusing using principal component analysis pca to form uncorrelated eigenclassifiers from a set of correlated experts combining the information from all classifiers may be better than subset selection where some base classifiers are pruned before combination because using all allows redundancy

a dynamic gradient approach to pareto optimization with nonsmooth convex objective functions in a general hilbert framework we consider continuous gradient like dynamical systems for constrained multiobjective optimization involving non smooth convex objective functions our approach is in the line of a previous work where was considered the case of convex di erentiable objective functions based on the yosida regularization of the subdi erential operators involved in the system we obtain the existence of strong global trajectories we prove a descent property for each objective function and the convergence of trajectories to weak pareto minima this approach provides a dynamical endogenous weighting of the objective functions applications are given to cooperative games inverse problems and numerical multiobjective optimization

second order forward backward dynamical systems for monotone inclusion problems we begin by considering second order dynamical systems of the from ddot x t gamma t dot x t lambda t b x t 0 where b cal h rightarrow cal h is a cocoercive operator defined on a real hilbert space cal h lambda 0 infty rightarrow 0 infty is a relaxation function and gamma 0 infty rightarrow 0 infty is a damping function both depending on time for the generated trajectories we show existence and uniqueness of the generated trajectories as well as their weak asymptotic convergence to a zero of the operator b the framework allows us to address from similar perspectives second order dynamical systems associated with the problem of finding zeros of the sum of a maximally monotone operator and a cocoercive one this captures as a particular case the minimization of the sum of a nonsmooth convex function with a smooth convex one furthermore we prove that when b is the gradient of a smooth convex function the value of the latter converges along the ergo

generalized solutions for the sum of two maximally monotone operators a common theme in mathematics is to define generalized solutions to deal with problems that potentially do not have solutions a classical example is the introduction of least squares solutions via the normal equations associated with a possibly infeasible system of linear equations in this paper we introduce a normal problem associated with finding a zero of the sum of two maximally monotone operators if the original problem admits solutions then the normal problem returns this same set of solutions the normal problem may yield solutions when the original problem does not admit any furthermore it has attractive variational and duality properties several examples illustrate our theory

multi objective evolutionary algorithms based on the summation of normalized objectives and diversified selection most multi objective evolutionary algorithms moeas use the concept of dominance in the search process to select the top solutions as parents in an elitist manner however as moeas are probabilistic search methods some useful information may be wasted if the dominated solutions are completely disregarded in addition the diversity may be lost during the early stages of the search process leading to a locally optimal or partial pareto front beside this the non domination sorting process is complex and time consuming to overcome these problems this paper proposes multi objective evolutionary algorithms based on summation of normalized objective values and diversified selection snov ds the performance of this algorithm is tested on a set of benchmark problems using both multi objective evolutionary programming moep and multi objective differential evolution mode with the proposed method the performance metric has improved significantly and the speed of the parent selection process has also increased when compared with the non domination sorting in addition the proposed algorithm also outperforms ten other algorithms

viscosity solutions of minimization problems viscosity methods for minimization problems are revisited from some modern perspectives in variational analysis variational convergences for sequences of functions epi convergence gamma convergence mosco convergence and for sequences of operators graph convergence provide a flexible tool for such questions it is proved in a rather large setting that the solutions of the approximate problems converge to a viscosity solution of the original problem that is a solution that is minimal among all the solutions with respect to some viscosity criteria various examples coming from mathematical programming calculus of variations semicoercive elliptic equations phase transition theory hamilton jacobi equations singular perturbations and optimal control theory are considered

convergence of damped inertial dynamics governed by regularized maximally monotone operators in a hilbert space setting we study the asymptotic behavior as time t goes to infinity of the trajectories of a second order differential equation governed by the yosida regularization of a maximally monotone operator with time varying positive index lambda t the dissipative and convergence properties are attached to the presence of a viscous damping term with positive coefficient gamma t a suitable tuning of the parameters gamma t and lambda t makes it possible to prove the weak convergence of the trajectories towards zeros of the operator when the operator is the subdifferential of a closed convex proper function we estimate the rate of convergence of the values these results are in line with the recent articles by attouch cabot and attouch peypouquet in this last paper the authors considered the case gamma t frac alpha t which is naturally linked to nesterov s accelerated method we unify and often improve the results already present in the literature

a multiobjective evolutionary programming framework for graph based data mining subgraph mining is the process of identifying concepts describing interesting and repetitive subgraphs within graph based data the exponential number of possible subgraphs makes the problem very challenging existing methods apply a single objective subgraph search with the view that interesting subgraphs are those capable of not merely compressing the data but also enhancing the interpretation of the data considerably usually the methods operate by posing simple constraints or user defined thresholds such as returning all subgraphs whose frequency is above a specified threshold such search approach may often return either a large number of solutions in the case of a weakly defined objective or very few in the case of a very strictly defined objective in this paper we propose a framework based on multiobjective evolutionary programming to mine subgraphs by jointly maximizing two objectives support and size of the extracted subgraphs the proposed methodology is able to discover a nondominated set of interesting subgraphs subject to tradeoff between the two objectives which otherwise would not be achieved by the single objective search besides it can use different specific multiobjective evolutionary programming methods experimental results obtained by three of the latter methods on synthetically generated as well as real life graph based datasets validate the utility of the proposed methodology when benchmarked against classical single objective methods and their previous nonevolutionary multiobjective extensions

differential evolution in constrained numerical optimization an empirical study motivated by the recent success of diverse approaches based on differential evolution de to solve constrained numerical optimization problems in this paper the performance of this novel evolutionary algorithm is evaluated three experiments are designed to study the behavior of different de variants on a set of benchmark problems by using different performance measures proposed in the specialized literature the first experiment analyzes the behavior of four de variants in 24 test functions considering dimensionality and the type of constraints of the problem the second experiment presents a more in depth analysis on two de variants by varying two parameters the scale factor f and the population size np which control the convergence of the algorithm from the results obtained a simple but competitive combination of two de variants is proposed and compared against state of the art de based algorithms for constrained optimization in the third experiment the study in this paper shows 1 important information about the behavior of de in constrained search spaces and 2 the role of this knowledge in the correct combination of variants based on their capabilities to generate simple but competitive approaches

a real coded genetic algorithm with a direction based crossover operator in this paper we develop a parallel structured real coded genetic algorithm rcga named the rga rdd for numerical optimization technically the proposed rga rdd integrates three specially designed evolutionary operators the ranking selection rs direction based crossover dbx and the dynamic random mutation drm as a whole to mimic a specific evolutionary process unlike the conventional rcgas that perform evolutionary operators in a series framework the rga rdd embeds a coordinator in the inner parallel loop to organize the operations of the dbx and drm so that a higher possibility of locating the global optimum is ensured besides based on the results of a systematic parametric analysis we provide a parameter selection guideline for the settings of the proposed rga rdd furthermore a data driven optimization scheme which incorporates the uniform design for design of experiments and a shape tunable neural network for auxiliary decision support is applied to search for an optimal set of the algorithm parameters the effectiveness and applicability of the proposed rga rdd are demonstrated through a variety of benchmarked optimization problems followed by comprehensive comparisons with some existing state of the art evolutionary algorithms extensive simulation results reveal that the performance of the proposed rga rdd is superior to comparative methods in locating the global optimum for real parameter optimization problems especially for unsolved multimodal and high dimensional hybrid functions

evolutionary programming kalman filter abstract a robust kalman filtering kf algorithm based on the evolutionary programming ep technique is proposed in this paper for uncertain systems with unknown but bounded uncertain parameters which are described by interval systems this algorithm takes advantage of the global optima searching capability of ep to find the optimal kf results at every iteration which include both the upper lower boundaries and the nominal trajectory of the optimal estimates of the system state vectors one prominent feature of this ep filtering algorithm is that it assumes the same statistical conditions and provides the same optimal estimates as the conventional kf scheme both linear and nonlinear systems are studied two typical computer simulation examples are given with comparison which verify the merits of the new method it yields more accurate estimation results and is less conservative as compared to the existing interval kalman filtering ikf