optimality and invexity in optimization problems in banach algebras spaces abstract in this paper we introduce into nonsmooth optimization theory in banach algebras a new class of mathematical programming problems which generalizes the notion of smooth kt p r invexity in fact this paper focuses on the optimality conditions for optimization problems in banach algebras regarding the generalized kt p r invexity notion and kuhn tucker points

p r invex sets and functions abstract notions of invexity of a function and of a set are generalized the notion of an invex function with respect to can be further extended with the aid of p invex sets slight generalization of the notion of p invex sets with respect to leads to a new class of functions a family of real functions called in general p r pre invex functions with respect to without differentiability or p r invex functions with respect to in the differentiable case is introduced some geometric properties of these classes of functions are derived sufficient optimality conditions are obtained for a nonlinear programming problem involving p r invex functions with respect to

equivalence of saddle points and optima and duality for a class of non smooth non convex problems abstract the equivalence between saddle points and optima and duality theorems are established for a much larger class of non smooth non convex problems in which functions are locally lipschitz and are satisfying invex type conditions of hanson and craven

hybrid filter banks with fractional delays minimax design and application to multichannel sampling this paper is motivated by multichannel sampling applications we consider a hybrid filter banks consisting of a set of fractional delays operators slow a d converters with different antialiasing filters digital expanders and digital synthesis filters to be designed the synthesis filters are designed to minimize the maximum gain of a hybrid induced error system we show that the induced error system is equivalent to a digital system this digital system enables the design of stable synthesis filters using existing control theory tools such as model matching and linear matrix inequalities moreover the induced error is robust against delay estimate errors numerical experiments show the proposed approach yields better performance compared to existing techniques

rigidity of asymptotically conical shrinking gradient ricci solitons we show that if two gradient shrinking ricci solitons are asymptotic along some end of each to the same regular cone 0 dr rg then the soliton metrics must be isometric on some neighborhoods of infinity of these ends our theorem imposes no restrictions on the behavior of the metrics off of the ends in question and in particular does not require their geodesic completeness as an application we prove that the only complete connected gradient shrinking ricci soliton asymptotic to a rotationally symmetric cone is the gaussian soliton on r

on p r invexity type nonlinear programming problems abstract mathematical programming problems involving p r invex functions with respect to are considered we introduce new classes of nonlinear programming problems called kt p r invex wd p r invex and hc p r invex problems where p r are some real numbers it is shown that for these types of problems kuhn tucker conditions are both necessary and sufficient for optimality furthermore these p r invexity type problems with r 0 are not sufficient for wolfe weak duality in this way it was shown that the optimization problems possessing some kind of invexity need not be equivalent to the class of optimization problems for which kuhn tucker necessary conditions for optimality are also sufficient and wolfe weak duality holds

a new approximation method for time delay systems we develop a rational approximant b sub n sup spl alpha of e sup ds and make a detailed analysis on the approximant b sub n sup spl alpha g of e sup ds g where g spl isin rl sup 2 we prove l sup p 2 spl infin error convergence and provide corresponding error bounds explicitly comparative study with other approximants is performed in order to make clear the properties of b sub n sup spl alpha making full use of its recursive structure b sub n sup spl alpha is shown to be a suitable approximant for a class of h sup spl infin problems involving time delay

manifolds with positive curvature operators are space forms the ricci flow was introduced by hamilton in 1982 h1 in order to prove that a compact three manifold admitting a riemannian metric of positive ricci curvature is a spherical space form in dimension four hamilton showed that compact four manifolds with positive curvature operators are spherical space forms as well h2 more generally the same conclusion holds for compact four manifolds with 2 positive curvature operators che recall that a curvature operator is called 2 positive if the sum of its two smallest eigenvalues is positive in arbitrary dimensions huisken hu described an explicit open cone in the space of curvature operators such that the normalized ricci flow evolves metrics whose curvature operators are contained in that cone into metrics of constant positive sectional curvature hamilton conjectured that in all dimensions compact riemannian manifolds with positive curvature operators must be space forms in this paper we confirm this conjecture more generally we show the following

optimality and duality for multiple objective optimization under generalized type i univexity abstract in this paper we extend the classes of generalized type i vector valued functions introduced by aghezzaf and hachimi in j global optim 18 2000 91 101 to generalized univex type i vector valued functions and consider a multiple objective optimization problem involving generalized type i univex functions a number of kuhn tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution the mond weir and general mond weir type duality results are also presented

necessary and sufficient conditions in constrained optimization additional conditions are attached to the kuhn tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization under appropriate constraint qualifications necessary and sufficient conditions are also given for optimality of the dual problem duality and converse duality are treated accordingly

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

model reduction of delay systems using pade approximants this paper describes the rational approximation of a certain class of delay systems in the frequency domain using pad approximants of exp st three classes of approximants characterized by their relative degrees are considered easily computable a priori l and l l2error bounds are provided

p r invexity in multiobjective programming abstract in this paper a generalization of convexity namely p r invexity is considered in the case of nonlinear multiobjective programming problems where the functions involved are differentiable the assumptions on pareto solutions are relaxed by means of p r invex functions also some duality results are obtained for such optimization problems

design of multirate filter banks by spl hscr sub spl infin optimization a procedure is developed to design iir synthesis filters in a multirate filter bank the filters minimize the l sub 2 induced norm of the error system between the multirate filter bank and a desired pure time delay system this criterion is reduced to one of spl hscr sub spl infin optimization for which there is ready made software

backward uniqueness for parabolic equations it is shown that a function u satisfying t u m u u u x t mem x 2 in n br 0 t and u x 0 0 for x n br must vanish identically in n br 0 t

linear periodic systems and multirate filter design we present a systematic procedure for the design of filters intended for multirate systems this procedure is motivated by viewing the equiripple design of filters in linear time invariant systems as a process of obtaining optimum minimax filters for a class of bounded energy input signals the philosophy of designing optimum minimax filters for classes of input signals is extended to multirate systems which are not time invariant we develop a generalized fourier analysis appropriate for linear periodic systems and use it to derive new error criteria for multirate filter design using such criteria yields optimum minimax multirate filters for the input signal class the utility of our method is demonstrated by using it to analyze several multirate systems we give numerical results on the design of a multirate implementation of a narrowband filter and compare our work to previous work on multirate filter design our numerical analysis is based upon a new formulation of the design as a semi infinite linear programming problem

real analyticity of solutions of hamilton s equation il existe des constantes positives cn et sn dependant seulement de la dimension n de la variete m telles que pour une metrique initiale g 0 avec r g 0 1 l equation de hamilton a une solution jusqu a t sn et l estimation suivante est vraie pour la metrique solution en t o t sn k 0 t k k 1 12 k r 2 c n

minimum rate sampling and reconstruction of signals with arbitrary frequency support we examine the question of reconstruction of signals from periodic nonuniform samples this involves discarding samples from a uniformly sampled signal in some periodic fashion we give a characterization of the signals that can be reconstructed at exactly the minimum rate once a nonuniform sampling pattern has been fixed we give an implicit characterization of the reconstruction system and a design method by which the ideal reconstruction filters may be approximated we demonstrate that for certain spectral supports the minimum rate can be approached or achieved using reconstruction schemes of much lower complexity than those arrived at by using spectral slicing as in earlier work previous work on multiband signals have typically been those for which restrictive assumptions on the sizes and positions of the bands have been made or where the minimum rate was approached asymptotically we show that the class of multiband signals which can be reconstructed exactly is shown to be far larger than previously considered when approaching the minimum rate this freedom allows us in certain cases to have a far less complex reconstruction system

reconstruction of irregularly sampled discrete time bandlimited signals with unknown sampling locations the purpose of this paper is to develop methods that can reconstruct a bandlimited discrete time signal from an irregular set of samples at unknown locations we define a solution to the problem using first a geometric and then an algebraic point of view we find the locations of the irregular set of samples by treating the problem as a combinatorial optimization problem we employ an exhaustive method and two descent methods the random search and cyclic coordinate methods the numerical simulations were made on three types of irregular sets of locations random sets sets with jitter around a uniform set and periodic nonuniform sets furthermore for the periodic nonuniform set of locations we develop a fast scheme that reduces the computational complexity of the problem by exploiting the periodic nonuniform structure of the sample locations in the dft

deforming the metric on complete riemannian manifolds soit m g ij x une variete de riemann a n dimensions complete non compacte de tenseur de complexe riemannien r ijkl satisfaisant r ijkl 2 k 0 sur m ou 0 0 dependant seulement de n et de k 0 telle que l equation d evolution g ij x t t 2r ij x t sur m g ij x o g ij x x m ait une solution lisse g ij x t 0 pour un temps court 0 t t u k 0 et satisfait l estimation suivante pour un entier m 0 il existe des constantes c m 0 dependant seulement de n m et k 0 telles que sup x m v m r ijkl x t 2 c m t m 0 t t u k 0