optimality for nonsmooth fractional multiple objective programming abstract in this study the necessary and sufficient optimality conditions for nonsmooth fractional multiple objective optimization problems are provided our idea is based on using the properties of limiting subdifferential vectors in nonsmooth analysis and a separation theorem in convex analysis

systematic encoding via grobner bases for a class of algebraic geometric goppa codes any linear code with a nontrivial automorphism has the structure of a module over a polynomial ring the theory of grobner bases for modules gives a compact description and implementation of a systematic encoder we present examples of algebraic geometric goppa codes that can be encoded by these methods including the one point hermitian codes

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

dynamic multi source x ray tomography using a spacetime level set method a novel variant of the level set method is introduced for dynamic x ray tomography the target is allowed to change in time while being imaged by one or several source detector pairs at a relatively high frame rate the algorithmic approach is motivated by the results in 22 showing that the modified level set method can tolerate highly incomplete projection data in stationary tomography furthermore defining the level set function in spacetime enforces temporal continuity in the dynamic tomography context considered here the tomographic reconstruction is found as a minimizer of a nonlinear functional the functional contains a regularization term penalizing the l 2 norms of up to n derivatives of the reconstruction the case n 1 is shown to be equivalent to a convex tikhonov problem that has a unique minimizer for n 2 the existence of a minimizer is proved under certain assumptions on the signal to noise ratio and the size of the regularization parameter numerical examples with both simulated and measured dynamic x ray data are included and the proposed method is found to yield reconstructions superior to standard methods such as fbp or non negativity constrained tikhonov regularization and favorably comparable to those of total variation regularization furthermore the methodology can be adapted to a wide range of measurement arrangements with one or more x ray sources

on the minimum distance of cyclic codes the main result is a new lower bound for the minimum distance of cyclic codes that includes earlier bounds i e bch bound ht bound roos bound this bound is related to a second method for bounding the minimum distance of a cyclic code which we call shifting this method can be even stronger than the first one for all binary cyclic codes of length with two exceptions we show that our methods yield the true minimum distance the two exceptions at the end of our list are a code and its even weight subcode we treat several examples of cyclic codes of length geq 63

multiple objective fractional programming involving semilocally type i preinvex and related functions abstract sufficient optimality conditions are obtained for a nonlinear multiple objective fractional programming problem involving semidifferentiable type i preinvex and related functions furthermore a general dual is formulated and duality results are proved under the assumptions of generalized semilocally type i preinvex and related functions our result generalize the results of preda v preda optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions j math anal appl 288 2003 365 382 and stancu minasian i m stancu minasian optimality and duality in fractional programming involving semilocally preinvex and related functions j inform optim sci 23 2002 185 201

composite nonsmooth programming with gâteaux differentiability this paper examines constrained nonsmooth optimization problems where the objective function and the constraints are compositions of locally lipschitz functions and g teaux differentiable functions but are not necessarily frechet differentiable or strict differentiable lagrangian necessary and sufficient optimality conditions are presented for various classes of composite programs these are obtained by constructing appropriate convex approximations for composite functions the lagrange multipliers are also characterized in terms of subgradients of the value function under appropriate conditions

apparent distance and a notion of bch multivariate codes this paper is devoted to studying two main problems 1 computing the apparent distance of an abelian code and 2 giving a notion of bose ray chaudhuri hocquenghem bch multivariate code to do this we first strengthen the notion of an apparent distance by introducing the notion of a strong apparent distance then we present an algorithm to compute the strong apparent distance of an abelian code based on some manipulations of hypermatrices associated with its generating idempotent our method uses less computations than those given by camion and sabin furthermore in the bivariate case the order of computation complexity is reduced from exponential to linear then we use our techniques to develop a notion of a bch code in the multivariate case and we extend most of the classical results on cyclic bch codes finally we apply our method to the design of abelian codes with maximum dimension with respect to a fixed apparent distance and a fixed length

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

uniformly bounded nemytskij operators between the banach spaces of functions of bounded n th variation abstract the main result says that the generator of any uniformly bounded composition operator acting between banach algebras of functions of bounded n th variation is an affine function with respect to the function variable

second order symmetric duality in mathematical programming with f convexity abstract under second order f convexity f concavity and second order f pseudoconvexity f pseudoconcavity appropriate second order duality results for pair of wolfe and mond weir type second order symmetric dual nonlinear programming problems are established these second order duality results are then used to formulate wolfe type and mond weir type second order minimax mixed integer dual programs and symmetric duality theorem is established under separability and second order f convexity f concavity of the kernel function f x y second order symmetric dual fractional mixed integer programs are studied using the above programs moreover second order self duality theorems for the above pairs are obtained assuming f x y to be skew symmetric

on optimality and duality for nonsmooth multiobjective fractional optimization problems abstract in this paper we consider a nonsmooth multiobjective fractional program for sufficient optimality conditions we define the nearly invex functions for locally lipschitz vector valued functions we obtain generalized sufficient optimality theorems and prove weak and strong duality theorems for the multiobjective fractional optimization problem involving nearly invex functions

optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions necessary and sufficient optimality conditions are obtained for a nonlinear fractional multiple objective programming problem involving semidifferentiable functions also a general dual is formulated and duality results are proved using concepts of generalized semilocally preinvex functions

representation theorem for local operators in the space of continuous and monotone functions we prove that every locally defined operator mapping the space of nondecreasing continuous functions into itself is a nemytskii composition operator

the concatenated structure of cyclic and abelian codes it is shown that a linear two dimensional cyclic code of length nn can be factorized into a direct sum of concatenated codes with cyclic inner and outer codes and conversely thai a two dimensional cyclic code can be constructed in this way this result is extended and it appears that the abelian codes are obtainable by taking a direct sum of several concatenations of cyclic codes codes are constructed that are better than any previously known in particular low rate cyclic codes superior to the duals of high rate bch codes are constructed

information sets from defining sets in abelian codes we describe a technique to construct a set of check positions and hence an information set for every abelian code solely in terms of its defining set this generalizes that given by imai in in the case of binary tdc codes

from ds bounds for cyclic codes to true minimum distance for abelian codes in this paper we develop a technique to extend any bound for the minimum distance of cyclic codes constructed from its defining sets ds bounds to abelian or multivariate codes through the notion of mathbb b apparent distance we also study conditions for an abelian code to verify that its mathbb b apparent distance reaches its true minimum distance then we construct some codes as an application

pre invex functions in multiple objective optimization and called such functions convexlike if s is a convex set and if f is a convex function then clearly f is convexlike elster and nehse obtained a saddlepoint optimality condition for convexlike mathematical programs hayashi and komiya 9 also considered convexlike functions and developed a gordan type theorem of the alternative involving convexlike functions and in addition considered lagrangian duality for convexlike programs hanson 7 considered differentiable functions f s r for which there exists an n dimensional vector function q q u such that for all x u e s