a new meta heuristic algorithm for continuous engineering optimization harmony search theory and practice most engineering optimization algorithms are based on numerical linear and nonlinear programming methods that require substantial gradient information and usually seek to improve the solution in the neighborhood of a starting point these algorithms however reveal a limited approach to complicated real world optimization problems if there is more than one local optimum in the problem the result may depend on the selection of an initial point and the obtained optimal solution may not necessarily be the global optimum this paper describes a new harmony search hs meta heuristic algorithm based approach for engineering optimization problems with continuous design variables this recently developed hs algorithm is conceptualized using the musical process of searching for a perfect state of harmony it uses a stochastic random search instead of a gradient search so that derivative information is unnecessary various engineering optimization problems including mathematical function minimization and structural engineering optimization problems are presented to demonstrate the effectiveness and robustness of the hs algorithm the results indicate that the proposed approach is a powerful search and optimization technique that may yield better solutions to engineering problems than those obtained using current algorithms 2004 elsevier b v all rights reserved

using sampling and simplex derivatives in pattern search methods in this paper we introduce ways of making a pattern search more efficient by reusing previous evaluations of the objective function based on the computation of simplex derivatives e g simplex gradients at each iteration one can attempt to compute an accurate simplex gradient by identifying a sampling set of previously evaluated points with good geometrical properties this can be done using only past successful iterates or by considering all past function evaluations the simplex gradient can then be used to reorder the evaluations of the objective function associated with the directions used in the poll step or to update the mesh size parameter according to a sufficient decrease criterion neither of which requires new function evaluations we present these procedures in detail and apply them to a set of problems from the cuter collection numerical results show that these procedures can enhance significantly the practical performance of pattern search methods

recent progress in unconstrained nonlinear optimization without derivatives we present an introduction to a new class of derivative free methods for unconstrained optimization we start by discussing the motivation for such methods and why they are in high demand by practitioners we then review the past developments in this field before introducing the features that characterize the newer algorithms in the context of a trust region framework we focus on techniques that ensure a suitable geometric quality of the considered models we then outline the class of algorithms based on these techniques as well as their respective merits we finally conclude the paper with a discussion of open questions and perspectives

mesh adaptive direct search algorithms for constrained optimization this paper addresses the problem of minimization of a nonsmooth function under general nonsmooth constraints when no derivatives of the objective or constraint functions are available we introduce the mesh adaptive direct search mads class of algorithms which extends the generalized pattern search gps class by allowing local exploration called polling in an asymptotically dense set of directions in the space of optimization variables this means that under certain hypotheses including a weak constraint qualification due to rockafellar mads can treat constraints by the extreme barrier approach of setting the objective to infinity for infeasible points and treating the problem as unconstrained the main gps convergence result is to identify limit points hat x where the clarke generalized derivatives are nonnegative in a finite set of directions called refining directions although in the unconstrained case nonnegative combinations of these directions span the whole space the fact that there can only be finitely many gps refining directions limits rigorous justification of the barrier approach to finitely many linear constraints for gps the main result of this paper is that the general mads framework is flexible enough to allow the generation of an asymptotically dense set of refining directions along which the clarke derivatives are nonnegative we propose an instance of mads for which the refining directions are dense in the hypertangent cone at hat x with probability 1 whenever the iterates associated with the refining directions converge to a single hat x the instance of mads is compared to versions of gps on some test problems we also illustrate the limitation of our results with examples

a simple robust and powerful test of the trend hypothesis abstract in this paper we develop a simple test procedure for a linear trend which does not require knowledge of the form of serial correlation in the data is robust to strong serial correlation and has a standard normal limiting null distribution under either i 0 or i 1 shocks in contrast to other available robust linear trend tests our proposed test achieves the gaussian asymptotic local power envelope in both the i 0 and i 1 cases for near i 1 errors our proposed procedure is conservative and a modification for this situation is suggested an estimator of the trend parameter together with an associated confidence interval which is asymptotically efficient again regardless of whether the shocks are i 0 or i 1 is also provided

an efficient constraint handling method for genetic algorithms many real world search and optimization problems involve inequality and or equality constraints and are thus posed as constrained optimization problems in trying to solve constrained optimization problems using genetic algorithms gas or classical optimization methods penalty function methods have been the most popular approach because of their simplicity and ease of implementation however since the penalty function approach is generic and applicable to any type of constraint linear or nonlinear their performance is not always satisfactory thus researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization however the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum in this paper ga s population based approach and ability to make pair wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter careful comparisons among feasible and infeasible solutions are made so as to provide a search direction towards the feasible region once sufficient feasible solutions are found a niching method along with a controlled mutation operator is used to maintain diversity among feasible solutions this allows a real parameter ga s crossover operator to continuously find better feasible solutions gradually leading the search near the true optimum solution gas with this constraint handling approach have been tested on nine problems commonly used in the literature including an engineering design problem in all cases the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier

essential self adjointness generalized eigenforms and spectra for the neumann problem on g manifolds let m be a complex manifold with boundary satisfying a subelliptic estimate which is also the total space of a principal g bundle with g a lie group and compact orbit space m g here we investigate the neumann laplacian on m we show that it is essentially self adjoint on its restriction to compactly supported smooth forms moreover we relate its spectrum to the existence of generalized eigenforms an energy belongs to if there is a subexponentially bounded generalized eigenform for this energy vice versa there is an expansion in terms of these well behaved eigenforms so that spectrally almost every energy comes with such a generalized eigenform

modeling an augmented lagrangian for blackbox constrained optimization constrained blackbox optimization is a difficult problem with most approaches coming from the mathematical programming literature the statistical literature is sparse especially in addressing problems with nontrivial constraints this situation is unfortunate because statistical methods have many attractive properties global scope handling noisy objectives sensitivity analysis and so forth to narrow that gap we propose a combination of response surface modeling expected improvement and the augmented lagrangian numerical optimization framework this hybrid approach allows the statistical model to think globally and the augmented lagrangian to act locally we focus on problems where the constraints are the primary bottleneck requiring expensive simulation to evaluate and substantial modeling effort to map out in that context our hybridization presents a simple yet effective solution that allows existing objective oriented statistical approaches like those based on gaussian process surrogates

a practicable contraction approach for the sum of the generalized polynomial ratios problem abstract in this paper a practicable contraction approach is proposed for solving the sum of the generalized polynomial ratios problem p with generalized polynomial constraints due to the intrinsic difficulty of problem p less work has been devoted to solving this problem the proposed approach is based on reducing the original nonconvex problem p as a standard geometric programming gp problem by utilizing simple transformation and contraction strategies the resulting optimization problem can be solved effectively by utilizing the solutions of a series of gp problems the tractability and effectiveness of the proposed successive contraction approach are demonstrated by several numerical examples and the performance comparison of the proposed approach and other methods published is also presented in terms of solution quality

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

global convergence of general derivative free trust region algorithms to first and second order critical points in this paper we prove global convergence for first and second order stationary points of a class of derivative free trust region methods for unconstrained optimization these methods are based on the sequential minimization of quadratic or linear models built from evaluating the objective function at sample sets the derivative free models are required to satisfy taylor type bounds but apart from that the analysis is independent of the sampling techniques a number of new issues are addressed including global convergence when acceptance of iterates is based on simple decrease of the objective function trust region radius maintenance at the criticality step and global convergence for second order critical points

metaheuristic vs deterministic global optimization algorithms the univariate case abstract many practical problems involve the search for the global extremum in the space of the system parameters the functions to be optimized are often highly multiextremal black box with unknown analytical representations and hard to evaluate even in the case of one parameter to be adjusted in the presence of non linear constraints the interest of both the stochastic in particular metaheuristic and mathematical programming in particular deterministic communities to the comparison of metaheuristic and deterministic classes of methods is well recognized although both the communities have a huge number of journal and proceedings papers a few of them are really dedicated to a systematic comparison of the methods belonging to these two classes this paper meets the requirement of such a comparison between nature inspired metaheuristic and deterministic algorithms more than 125 000 launches of the methods have been performed and presents an attempt beneficial to practical fields including engineering design to bring together two rather disjoint communities of metaheuristic and mathematical programming researchers and applied users

orbit optimization by radial basis function interpolation in trust regions we present a new derivative free algorithm orbit for unconstrained local optimization of computationally expensive functions a trust region framework using interpolating radial basis function rbf models is employed the rbf models considered often allow orbit to interpolate nonlinear functions using fewer function evaluations than the polynomial models considered by present techniques approximation guarantees are obtained by ensuring that a subset of the interpolation points is sufficiently poised for linear interpolation the rbf property of conditional positive definiteness yields a natural method for adding additional points we present numerical results on test problems to motivate the use of orbit when only a relatively small number of expensive function evaluations are available results on two very different application problems calibration of a watershed model and optimization of a pde based bioremediation plan are also encouraging and support orbit s effectiveness on blackbox functions for which no special mathematical structure is known or available

an improved harmony search algorithm for solving optimization problems this paper develops an improved harmony search ihs algorithm for solving optimization problems ihs employs a novel method for generating new solution vectors that enhances accuracy and convergence rate of harmony search hs algorithm in this paper the impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented the ihs algorithm has been successfully applied to various benchmarking and standard engineering optimization problems numerical results reveal that the proposed algorithm can find better solutions when compared to hs and other heuristic or deterministic methods and is a powerful search algorithm for various engineering optimization problems

geometry of interpolation sets in derivative free optimization we consider derivative free methods based on sampling approaches for nonlinear optimization problems where derivatives of the objective function are not available and cannot be directly approximated we show how the bounds on the error between an interpolating polynomial and the true function can be used in the convergence theory of derivative free sampling methods these bounds involve a constant that reflects the quality of the interpolation set the main task of such a derivative free algorithm is to maintain an interpolation sampling set so that this constant remains small and at least uniformly bounded this constant is often described through the basis of lagrange polynomials associated with the interpolation set we provide an alternative more intuitive definition for this concept and show how this constant is related to the condition number of a certain matrix this relation enables us to provide a range of algorithms whilst maintaining the interpolation set so that this condition number or the geometry constant remain uniformly bounded we also derive bounds on the error between the model and the function and between their derivatives directly in terms of this condition number and of this geometry constant

an information global optimization algorithm with local tuning we propose an algorithm using only the values of the objective function for solving unconstrained global optimization problems this algorithm belongs to the class of the information methods introduced by strongin numerical methods in multiextremal problems nauka moskow 1978 and differs from the other algorithms of this class by the presence of local tuning which spies on the changes of the lipschitz constant of the objective function over different sectors of the search region we describe two versions of the method for solving one dimensional problems and for solving multidimensional problems using peano type space filling curves for reduction of imensionality in both cases we establish sufficient conditions of convergence to the global minimum we also report results of some numerical experiments

optimal tests when a nuisance parameter is present only under the alternative this paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null for example the results apply to tests of structural change with unknown changepoint the testing problem considered is nonstandard and the classical asymptotic optimality results for the lagrange multiplier wald and likelihood ratio do not apply a weighted average power criterion is used here to generate optimal tests this criterion is similar to that used by a wald 1943 to obtain the classical asymptotic optimality properties of wald tests in regular testing problems copyright 1994 by the econometric society

optimization by direct search new perspectives on some classical and modern methods direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis nonetheless users remained loyal to these methods most of which were easy to program some of which were reliable in the past fifteen years these methods have seen a revival due in part to the appearance of mathematical analysis as well as to interest in parallel and distributed com puting this review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results the underlying principles allow general ization to handle bound constraints and linear constraints we also discuss extensions to problems with nonlinear constraints

lipschitz gradients for global optimization in a one point based partitioning scheme a global optimization problem is studied where the objective function f x is a multidimensional black box function and its gradient f x satisfies the lipschitz condition over a hyperinterval with an unknown lipschitz constant k different methods for solving this problem by using an a priori given estimate of k its adaptive estimates and adaptive estimates of local lipschitz constants are known in the literature recently the authors have proposed a one dimensional algorithm working with multiple estimates of the lipschitz constant for f x the existence of such an algorithm was a challenge for 15 years in this paper a new multidimensional geometric method evolving the ideas of this one dimensional scheme and using an efficient one point based partitioning strategy is proposed numerical experiments executed on 800 multidimensional test functions demonstrate quite a promising performance in comparison with popular direct based methods

global search based on efficient diagonal partitions and a set of lipschitz constants in the paper the global optimization problem of a multidimensional black box function satisfying the lipschitz condition over a hyperinterval with an unknown lipschitz constant is considered a new efficient algorithm for solving this problem is presented at each iteration of the method a number of possible lipschitz constants are chosen from a set of values varying from zero to infinity this idea is unified with an efficient diagonal partition strategy a novel technique balancing usage of local and global information during partitioning is proposed a new procedure for finding lower bounds of the objective function over hyperintervals is also considered it is demonstrated by extensive numerical experiments performed on more than 1600 multidimensional test functions that the new algorithm shows a very promising performance

local tuning and partition strategies for diagonal go methods in this paper global optimization go lipschitz problems are considered where the multi dimensional multiextremal objective function is determined over a hyperinterval an efficient one dimensional go method using local tuning on the behavior of the objective function is generalized to the multi dimensional case by the diagonal approach using two partition strategies global convergence conditions are established for the obtained diagonal geometric methods results of a wide numerical comparison show a strong acceleration reached by the new methods working with estimates of the local lipschitz constants over different subregions of the search domain in comparison with the traditional approach

convergence properties of the nelder mead simplex method in low dimensions the nelder mead simplex algorithm first published in 1965 is an enormously popular direct search method for multidimensional unconstrained minimization despite its widespread use essentially no theoretical results have been proved explicitly for the nelder mead algorithm this paper presents convergence properties of the nelder mead algorithm applied to strictly convex functions in dimensions 1 and 2 we prove convergence to a minimizer for dimension 1 and various limited convergence results for dimension 2 a counterexample of mckinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the nelder mead algorithm converges to a nonminimizer it is not yet known whether the nelder mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions

the complex green operator on cr submanifolds of ℂⁿ of hypersurface type compactness we establish compactness estimates for b on a compact pseudoconvex cr submanifold of c of hypersurface type that satisfies property p when the submanifold is orientable these estimates were proved by a raich in 32 using microlocal methods our proof deduces the estimates from a slight extension when q 1 of those known on hypersurfaces via the fact that locally cr submanifolds of hypersurface type are cr equivalent to a hypersurface the relationship between two potential theoretic conditions is also clarified

revisiting asynchronous parallel pattern search for nonlinear optimization we present a new asynchronous parallel pattern search apps method which is different from that developed previously by hough kolda and torczon apps efficiently uses parallel and distributed computing platforms to solve science and engineering design optimization problems where derivatives are unavailable and cannot be approximated the original apps was designed to be fault tolerant as well as asynchronous and was based on a peer to peer design each process was in charge of a single fixed search direction our new version is based instead on a manager worker paradigm though less fault tolerant the resulting algorithm is more flexible in its use of distributed computing resources we further describe how to incorporate a zero order sufficient decrease condition and handle bound constraints convergence theory for all situations unconstrained and bound constrained as well as simple and sufficient decrease is developed we close with a discussion of how the new apps will better facilitate the future incorporation of linear and nonlinear constraints

index information algorithm with local tuning for solving multidimensional global optimization problems with multiextremal constraints multidimensional optimization problems where the objective function and the constraints are multiextremal non differentiable lipschitz functions with unknown lipschitz constants and the feasible region is a finite collection of robust nonconvex subregions are considered both the objective function and the constraints may be partially defined to solve such problems an algorithm is proposed that uses peano space filling curves and the index scheme to reduce the original problem to a holder one dimensional one local tuning on the behaviour of the objective function and constraints is used during the work of the global optimization procedure in order to accelerate the search the method neither uses penalty coefficients nor additional variables convergence conditions are established numerical experiments confirm the good performance of the technique

estimating deterministic trends with an integrated or stationary noise component abstract we propose a test for the slope of a trend function when it is a priori unknown whether the series is trend stationary or contains an autoregressive unit root the procedure is based on a feasible quasi generalized least squares method from an ar 1 specification with parameter the sum of the autoregressive coefficients the estimate of is the ols estimate obtained from an autoregression applied to detrended data and is truncated to take a value 1 whenever the estimate is in a t neighborhood of 1 this makes the estimate super efficient when 1 and implies that inference on the slope parameter can be performed using the standard normal distribution whether 1 or 1 theoretical arguments and simulation evidence show that 1 2 is the appropriate choice simulations show that our procedure has better size and power properties than the tests proposed by bunzel h vogelsang t j 2005 powerful trend function tests that are robust to strong serial correlation with an application to the prebish singer hypothesis journal of business and economic statistics 23 381 394 and harvey d i leybourne s j taylor a m r 2007 a simple robust and powerful test of the trend hypothesis journal of econometrics 141 1302 1330

mixed variable engineering optimization based on evolutionary and social metaphors the co existence of discrete and continuous independent variables in an engineering optimization problem with a multimodal objective function makes many methods incapable of solving the problem four methods are tested here a a simple genetic algorithm sga b a struggle genetic algorithm strga c a particle swarm optimization algorithm psoa and d a particle swarm optimization algorithm with struggle selection psostr the last one has been developed by the author and it is a hybrid of the evolutionary strga and the socially inspired psoa they are tested in four purely mathematical and three engineering optimization problems of the aforementioned type all of the methods solved successfully all the problems and located the global optimum the psostr however outperformed the other methods in terms of both solution accuracy and computational cost i e function evaluations

boundary invariants of pseudoconvex domains the purpose of this paper is to describe an invariant ax z which is associated with each point z in the boundary of a smoothly bounded pseudoconvex domain in cn the motivation for defining the invariant ax z referred to as the multitype of z comes from the study of the boundary regularity properties of solutions of the d neumann problem on domains of finite type by a domain of finite type we mean one that satisfies the definition given by d angelo 5 namely a domain such that at any boundary point the maximum order of contact of one dimensional complex analytic varieties with the boundary is bounded in 4 the author showed how one can give a proof of global regularity of the a neumann problem for pseudoconvex domains of finite type if there is an invariant such as the one described in this paper in a forthcoming article this invariant will be used to obtain a proof of subelliptic estimates for the same class of domains before giving the definition of the multitype ax z we must introduce some

acceleration of univariate global optimization algorithms working with lipschitz functions and lipschitz first derivatives this paper deals with two kinds of the one dimensional global optimization problem over a closed finite interval i the objective function f x satisfies the lipschitz condition with a constant l ii the first derivative of f x satisfies the lipschitz condition with a constant m in the paper six algorithms are presented for the case i and six algorithms for the case ii in both cases auxiliary functions are constructed and adaptively improved during the search in the case i piecewise linear functions are constructed and in the case ii smooth piecewise quadratic functions are used the constants l and m either are taken as values known a priori or are dynamically estimated during the search a recent technique that adaptively estimates the local lipschitz constants over different zones of the search region is used to accelerate the search a new technique called the local improvement is introduced in order to accelerate the search in both cases i and ii the algorithms are

a general formula for eigenvalue assignment by static output feedback with application to robust design in this note generalizing an idea of a previous paper we derive a new expression of the characteristic polynomial of a linear system subject to static output feedback from this expression an explicit form of the assignment equations in the unknown elements of the feedback matrix is obtained the equations are completely general and seem much simpler than many others proposed until now in special cases a closed or almost a closed form solution is obtained the assignment equations are then used within an algorithm for global optimization to solve the problem of exactly assigning the eigenvalues of the nominal plant while maximizing the norm of perturbation matrices for which the perturbed eigenvalues remain in specified regions of the complex plane

uobyqa unconstrained optimization by quadratic approximation uobyqa is a new algorithm for general unconstrained optimization calculations that takes account of the curvature of the objective function f say by forming quadratic models by interpolation therefore because no first derivatives are required each model is defined by n 1 n 2 values of f where n is the number of variables and the interpolation points must have the property that no nonzero quadratic polynomial vanishes at all of them a typical iteration of the algorithm generates a new vector of variables widetilde underline x t say either by minimizing the quadratic model subject to a trust region bound or by a procedure that should improve the accuracy of the model then usually f widetilde underline x t is obtained and one of the interpolation points is replaced by widetilde underline x t therefore the paper addresses the initial positions of the interpolation points the adjustment of trust region radii the calculation of widetilde underline x t in the two cases that have been mentioned and the selection of the point to be replaced further uobyqa works with the lagrange functions of the interpolation equations explicitly so their coefficients are updated when an interpolation point is moved the lagrange functions assist the procedure that improves the model and also they provide an estimate of the error of the quadratic approximation to f which allows the algorithm to achieve a fast rate of convergence these features are discussed and a summary of the algorithm is given finally a fortran implementation of uobyqa is applied to several choices of f in order to investigate accuracy robustness in the presence of rounding errors the effects of first derivative discontinuities and the amount of work the numerical results are very promising for n 20 but larger values are problematical because the routine work of an iteration is of fourth order in the number of variables

hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems this study presents a hybrid harmony search algorithm hhsa to solve engineering optimization problems with continuous design variables although the harmony search algorithm hsa has proven its ability of finding near global regions within a reasonable time it is comparatively inefficient in performing local search in this study sequential quadratic programming sqp is employed to speed up local search and improve precision of the hsa solutions moreover an empirical study is performed in order to determine the impact of various parameters of the hsa on convergence behavior various benchmark engineering optimization problems are used to illustrate the effectiveness and robustness of the proposed algorithm numerical results reveal that the proposed hybrid algorithm in most cases is more effective than the hsa and other meta heuristic or deterministic methods

two methods for solving optimization problems arising in electronic measurements and electrical engineering in this paper we introduce a common problem in electronic measurements and electrical engineering finding the first root from the left of an equation in the presence of some initial conditions we present examples of electrotechnical devices analog signal filtering where it is necessary to solve it two new methods for solving this problem based on global optimization ideas are introduced the first uses the exact a priori given global lipschitz constant for the first derivative the second method adaptively estimates local lipschitz constants during the search both algorithms either find the first root from the left or determine the global minimizers in the case when the objective function has no roots sufficient conditions for convergence of the new methods to the desired solution are established in both cases the results of numerical experiments for real problems and a set of test functions are also presented

comparison of the bergman and szego kernels abstract the quotient of the szego and bergman kernels for a smooth bounded pseudoconvex domains in c n is bounded from above by a constant multiple of log p for any p n where is the distance to the boundary for a class of domains that includes those of d angelo finite type and those with plurisubharmonic defining functions the quotient is also bounded from below by a constant multiple of log p for any p 1 moreover for convex domains the quotient is bounded from above and below by constant multiples of

global convergence of radial basis function trust region algorithms for derivative free optimization we analyze globally convergent derivative free trust region algorithms relying on radial basis function interpolation models our results extend the recent work of conn scheinberg and vicente siam j optim 20 2009 pp 387 415 to fully linear models that have a nonlinear term we characterize the types of radial basis functions that fit in our analysis and thus show global convergence to first order critical points for the orbit algorithm of wild regis and shoemaker siam j sci comput 30 2008 pp 3197 3219 using orbit we present numerical results for different types of radial basis functions on a series of test problems we also demonstrate the use of orbit in finding local minima on a computationally expensive environmental engineering problem involving remediation of contaminated groundwater

real hypersurfaces orders of contact and applications a fundamental problem in the modem theory of several complex variables concerns the boundary behavior of the cauchy riemann equations suppose that d is an open domain in cn and that its boundary m is a smooth real submanifold of cn how does the geometry of m influence the function theory on d one approach to this question is the a neumann problem 6 there one studies the inhomogeneous cauchy riemann equations au a where a is a 0 q form with distribution coefficients on the closed domain d u m satisfying the necessary compatibility condition a a 0 the a neumann problem constructs a particular solution u which is orthogonal to the null space of the complex laplacian kohn 10a has solved this problem and has shown that good local regularity properties for u in terms of a follow from so called subelliptic estimates it is natural to seek geometric conditions on m that are necessary and sufficient for these estimates in this paper we will be concerned with a certain geometric condition on m that we feel is the right one for subellipticity although the motivation for the questions discussed here comes from partial differential equations the techniques come from algebraic geometry to see why we state theorems of kohn greiner and catlin concerning subellipticity kohn 1oa has discovered a sufficient condition for a subelliptic estimate near a fixed point p in m in case d is pseudoconvex and is contained in c2 this condition is equivalent to the finiteness of order of tangency of every complex analytic one dimensional manifold with m at p greiner 13 established the necessity of this condition in

weighted bergman kernels and quantization let be a bounded pseudoconvex domain in c n two positive functions on such that log log are plurisubharmonic and z a point at which log is smooth and strictly plurisubharmonic we show that as k the bergman kernels with respect to the weights k have an asymptotic expansion for x y near z where x y is an almost analytic extension of phi x x x and similarly for further if in addition is of finite type behave reasonably at the boundary and log log are strictly plurisubharmonic on we obtain also an analogous asymptotic expansion for the berezin transform and give applications to the berezin quantization finally for smoothly bounded and strictly pseudoconvex and a smooth strictly plurisubharmonic defining function for we also obtain results on the berezin toeplitz quantization

analytic discs plurisubharmonic hulls and non compactness of the neumann operator we show that a complex manifold m in the boundary of a smooth bounded pseudoconvex domain in open image in new window is an obstruction to compactness of the open image in new window neumann operator on provided that at some point of m the levi form of b has the maximal possible rank n 1 dim m i e the boundary is strictly pseudoconvex in the directions transverse to m in particular an analytic disc is an obstruction provided that at some point of the disc the levi form has only one zero eigenvalue i e the eigenvalue zero has multiplicity one we also show that a boundary point where the levi form has only one zero eigenvalue can be picked up by the plurisubharmonic hull of a set only via an analytic disc in the boundary

weakly pseudoconvex domains with non compact automorphism groups the purpose of this paper is to prove a uniform extendibility result for sequences of biholomorphic mappings between weakly pseudoconvex domains suppose that f21 and 02 are bounded weakly pseudoconvex domains in e with real analytic boundaries and suppose that fi is a sequence of biholomorphic mappings j i2t o2 which converges to a holomorphic mapping f of 2 into the closure of 122 we remark that a strictly pseudoconvex domain is not a weakly pseudoconvex domain cartan s theorem states that either f is a biholomorphic map of f2 onto 02 or f is a mapping of f21 into the boundary of f22 we shall prove that in either case there exists a domain d which contains 121 together with all the strictly pseudoconvex boundary points of f2x such that each of the mappings f extend to be hoiomorphic on d furthermore the limit map fextends holomorphically to d and the sequence fi converges uniformly on compact subsets of d to f it is interesting to note that the corresponding statement for a sequence of maps between strictly pseudoconvex domains with real analytic boundaries is not true indeed if i21 is strictly pseudoconvex and the limit map f maps into bf22 then both o t and i22 are biholomorphic to the ball by wong s theorem in this situation if the inverse mappings fi f 1 also converge then there is an open set d which contains the closure of o1 minus a single point in bf21 to which all the f extend and the sequence f converges uniformly on compact subsets of d to f if no assumption is made about the convergence of the inverses then the maps need not converge uniformly up to the boundary near any boundary point of o1 when f21 and 02 are assumed to be weakly pseudoconvex and therefore not biholomorphic to the ball the assumption about the convergence of the inverse maps is not needed

extension of c r structures on three dimensional compact pseudoconvex c r manifolds let m be a smooth compact orientable pseudoconvex c r manifold of real dimension three and assume that there is a smooth function which is strictly subharmonic in any direction where the levi form vanishes on m then we extend the given c r structure on m to an integrable almost complex structure on the concave side of m as an application if m is a non compact pseudoconvex c r manifold of real dimension three we prove that the given c r structure on m can be locally extended to an integrable almost complex structure on the concave side of m

benchmarking derivative free optimization algorithms we propose data profiles as a tool for analyzing the performance of derivative free optimization solvers when there are constraints on the computational budget we use performance and data profiles together with a convergence test that measures the decrease in function value to analyze the performance of three solvers on sets of smooth noisy and piecewise smooth problems our results provide estimates for the performance difference between these solvers and show that on these problems the model based solver tested performs better than the two direct search solvers tested

local extension of boundary holomorphic forms on real hypersurfaces in cn abstract let m be a real hypersurface in c n with n 3 and the levi form at p m has q 1 positive eigenvalues 1 q n 2 we solve one sided local closed extension problem near p for 0 r forms for 1 r q

a new approximate point optimal test of a composite null hypothesis in this paper we use the generalized neyman pearson lemma to introduce a new approximate point optimal test that can be used for testing a composite null hypothesis against a composite alternative the new test involves finding multiple critical values two methods for obtaining these critical values are outlined we report simulations of the application of this test to two composite non nested testing problems namely testing for first order moving average ma 1 errors against first order autoregressive ar 1 errors in the linear regression model and testing for ar 1 errors against integrated ma 1 ima 1 1 errors in the linear model we compare the performance of the new test with silvapulle and king s 1991 approximate point optimal test and some asymptotic tests and find that the new test has a clear advantage over the other tests particularly for the second testing problem

derivative free robust optimization by outer approximations we develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives the algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite cardinality uncertainty set clarke stationarity of the algorithm output is established alongside desirable features of the model based trust region subproblems encountered we demonstrate the practical benefits of the algorithm on a new class of test problems

testing for a trend with persistent errors abstract we develop new tests for the coefficient on a time trend in a regression of a variable on a constant and time trend where there is potentially strong serial correlation this serial correlation can also include a unit root we obtain tests under two different assumptions on the initial value for the stochastic component of the variable being examined either this being zero asymptotically and also allowing the initial condition to be drawn from its unconditional distribution we find that statistics perform better under the second of these assumptions which is the more natural assumption to make

a hybrid pso ga algorithm for constrained optimization problems the main objective of this paper is to present a hybrid technique named as a pso ga for solving the constrained optimization problems in this algorithm particle swarm optimization pso operates in the direction of improving the vector while the genetic algorithm ga has been used for modifying the decision vectors using genetic operators the balance between the exploration and exploitation abilities have been further improved by incorporating the genetic operators namely crossover and mutation in pso algorithm the constraints defined in the problem are handled with the help of the parameter free penalty function the experimental results of constrained optimization problems are reported and compared with the typical approaches exist in the literature as shown the solutions obtained by the proposed approach are superior to those of existing best solutions reported in the literature furthermore experimental results indicate that the proposed approach may yield better solutions to engineering problems than those obtained by using current algorithms

technical communique a global optimization technique for checking parametric robustness this note investigates the possibilities offered by a novel global optimization technique in solving some minimization problems arising in control theory the technique is described and some applications to typical control problems are reported

duality and approximation of bergman spaces abstract expected duality and approximation properties are shown to fail on bergman spaces of domains in c n via examples when the domain admits an operator satisfying certain mapping properties positive duality and approximation results are proved such operators are constructed on generalized hartogs triangles on a general bounded reinhardt domain norm convergence of laurent series of bergman functions is shown this extends a classical result on hardy spaces of the unit disc