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

a direct approach to generation of analytic semigroups by generalized ornstein uhlenbeck operators in weighted lp spaces abstract generation of analytic semigroups by generalized ornstein uhlenbeck operators a g v in the weighted space l p r n e x d x is shown the results improve the recent results established by metafune pruss rhandi schnaubelt 2005 8 v 0 and kojima yokota 2010 6 v 0 the proofs of those are based on a generation result acting on the unweighted space l p r n 8 theorem 3 4 while ours is carried out by an application of l p theory for second order elliptic operators 13 theorem 1 3 obtained by sobajima 2012 consequently the additional condition div g e 2 v c e assumed in both 8 6 is completely removed

elliptic operators on rd with unbounded coefficients u t t x 1 2 tr c x du t x f x du t x 1 2 u 0 x x if the coefficients c and f are continuous and bounded and c is nondegenerate then a satisfactory theory of both equations is available see 18 15 the situation changes dramatically when the coefficients f and c are unbounded in this case even uniqueness of solutions becomes problematic as shown by the example 2 xxx see 20 the main goal of this paper is to study equations 1 1 and 1 2 in case of unbounded f and c we will consider well posedness of problems 1 1 doi 10 1006 jdeq 2000 3866 available online at http www idealibrary com on

duality for multiple objective convex programs a duality theory for the problem of finding the properly efficient values of a multiple objective convex program is obtained using arguments and concepts analogous to those used by rockafellar for scalar valued problems a key result is that xi minimizes a convex vector valued function f if and only if there is a zero like subgradient of f at xi consequently if a vector valued convex program with a given perturbation is represented by a convex bifunction then the properly efficient values of the program are equal to the perturbation function evaluated at zero like perturbations a dual program is defined in terms of the adjoint bifunction certain closure conditions insure the absence of a duality gap the dual variables are matrices with the interpretation that the i j th element is the value of the ith resource in terms of the jth objective a concept of optimality called isermann efficiency is introduced and compared with efficiency and proper efficiency isermann efficiency generalizes a concept from isermann s work on multiple objective linear programs

geometric duality in multiple objective linear programming we develop in this article a geometric approach to duality in multiple objective linear programming this approach is based on a very old idea the duality of polytopes which can be traced back to the old greeks we show that there is an inclusion reversing one to one map between the minimal faces of the image of the primal objective and the maximal faces of the image of the dual objective map

matrix traces on c algebra mn a abstract in this note for a c algebra a we define a matrix trace on the c algebra m n a to be a positive linear mapping m n a a such that u au a a m n a u u m n a and a 2 a 2 a 0 we give some basic properties of a matrix trace and prove that if a is a unital abelian c algebra then a map is an a module matrix trace on m n a if and only if there exists an element of a with 0 2 such that a tr a a a ij m n a where tr a i 1 n a ii

on supremum of a set in a multi dimensional space on donne une definition exacte du supremum d un ensemble dans l espace euclidien a n dimensions etendu et on montre qu elle est presque equivalente a celle proposee par kawasaki 1982 on etudie certaines proprietes de ce supremum ce qui pourra etre utile pour developper une theorie de dualite conjuguee en optimisation vectorielle

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

optimality and duality in multiobjective fractional programming involving ρ semilocally type i preinvex and related functions abstract optimality conditions are obtained for a nonlinear fractional multiobjective programming problem involving semidifferentiable functions also a general dual is formulated and a duality result is proved using concepts of generalized semilocally type i preinvex functions

generation of analytic semigroups by generalized ornstein uhlenbeck operators with potentials it is shown that the generalized ornstein uhlenbeck operator with potential a g vu u u g u vu with suitable domain generates an analytic semigroup on the weighted space lp rn 1 p where dx e dx the result extends the generation theorem established by metafune pruss rhandi schnaubelt when v 0 to the case where v 0 while the proof is based on their useful theorem that a class of second order elliptic operators generates an analytic semigroup on the unweighted space lp rn

duality theory for the matrix linear programming problem multiple objective linear programming also known as the linear vector maximization problem has been studied by a number of authors in particular its duality theory has been considered by philip 9 isermann 7 gray and sutherland 5 brumelle 11 and ponstein lo neither the symmetry nor all the relationships of the duality theory of conventional linear programming however have been obtained in previous work such results are developed in this paper which is most directly related to 7 by regarding the variables to be matrices previous work on matrix linear programming 3 has been restricted to a scalar objective function and differs substantially from that presented here the notation r will denote the real inner product space of all real m x n matrices a ai and as usual r will be written for r x 1 r lx will be the set of matrices in r with all nonnegative elements and e rnlxn the matrix consisting entirely of zeros with its order apparent from context for a b e rmxn wewritea a ifb aer i 0 the relation is obviously a partial order on r x n let s be a subset of r m x n the point z e s is said to be a maximal element or upper efficient point of s if there does not exist z e s for which z z similarly z e s is a minimal element or lower efficient point of s if there does not exist z e s for which z z the set of all maximal elements of s is denoted by max s and minimal elements by min s

υ preinvexity and υ invexity in mathematical programming in the paper we introduce and characterize a new class of nonconvex functions in mathematical programming named c preinvex functions which are called c invex functions in the case of differentiability the class of c reinvex functions is wider than that of preinvex functions and thus in the case of differentiability than the class of invex functions some optimality results are obtained under c preinvexity assumption for a constrained optimization problem with not necessarily differentiable functions further a number of sufficiency conditions and wolfe duality theorems are established under c invexity assumption an alternative approach with a modified c invexity notion to optimality conditions and duality results is also considered

an efficient robust adaptive filtering algorithm based on parallel subgradient projection techniques this paper presents a novel robust adaptive filtering scheme based on the interactive use of statistical noise information and the ideas developed originally for efficient algorithmic solutions to the convex feasibility problems the statistical noise information is quantitatively formulated as stochastic property closed convex sets by the simple design formulae developed in this paper a simple set theoretic inspection also leads to an important statistical reason for the sensitivity to noise of the affine projection algorithm apa the proposed adaptive algorithm is computationally efficient and robust to noise because it requires only an iterative parallel projection onto a series of closed half spaces that are highly expected to contain the unknown system to be identified and is free from the computational load of solving a system of linear equations the numerical examples show that the proposed adaptive filtering scheme realizes dramatically fast and stable convergence for highly colored excited speech like input signals in severe noise situations

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

a matrix trace inequality abstract in this note the matrix trace inequality for positive semidefinite matrices a and b tr ab m tr a 2 m tr b 2 m 1 2 is established where m is an integer the above inequality improves the result given by yang j math anal appl 250 2000 372 374

a matrix trace inequality for products of hermitian matrices abstract in this note the following matrix trace inequality for products of hermitian matrices a and b tr ab 2 k tr a 2 k b 2 k is established where k is an integer the above inequality also partly answers a conjecture in bellman in proceedings of the 2nd international conference on general inequalities e f beckenbach ed pp 89 90 birkhauser basel 1980

duality theory for maximizations with respect to cones generalizations of pareto optimality have been studied by a number of authors in finite dimensions such work is exemplified by corley s 1 dacunha and polak lo goeffrion 131 hartley 151 lin 171 tanino and sawaragi 1211 wendell and lee 22 and yu 23 the optimization of functions into possibly infinite dimensions has been considered by borwein 121 cesari and suryanarayana 3 christopeit 4 corley 6 7 craven s 91 hurwicz 16 1 neustadt 19 1 and ritter 20 an extensive bibliography on pareto optimality its extensions and applications is given in 111 in this paper a duality theory is developed using the concept of saddlepoints for a problem in which the maximization of a function into possibly infinite dimensions is defined in terms of a cone the results here extend the work of tanino and sawaragi 21 to infinite dimensions a distinction is also made here between the notions of weak and strong optimality distinguishing between the two concepts allows the removal of the assumption of properness in 211 in establishing a relationship between the primal and dual problems as well as permits additional duality relationships to be proved

online sparse system identification and signal reconstruction using projections onto weighted ell_ 1 balls this paper presents a novel projection based adaptive algorithm for sparse signal and system identification the sequentially observed data are used to generate an equivalent sequence of closed convex sets namely hyperslabs each hyperslab is the geometric equivalent of a cost criterion that quantifies data mismatch sparsity is imposed by the introduction of appropriately designed weighted l1 balls and the related projection operator is also derived the algorithm develops around projections onto the sequence of the generated hyperslabs as well as the weighted l1 balls the resulting scheme exhibits linear dependence with respect to the unknown system s order on the number of multiplications additions and an o llog2l dependence on sorting operations where l is the length of the system signal to be estimated numerical results are also given to validate the performance of the proposed method against the least absolute shrinkage and selection operator lasso algorithm and two very recently developed adaptive sparse schemes that fuse arguments from the lms rls adaptation mechanisms with those imposed by the lasso rational

a matrix trace inequality abstract in a short note y yang 2 solved a problem set by r bellman 1 it is not difficult to prove a slightly relaxed version of yang s result we shall use a different method

asymptotic achievability of the cramer rao bound for noisy compressive sampling we consider a model of the form y ax n where x isin cm is sparse with at most l nonzero coefficients in unknown locations y isin cn is the observation vector a isin cn times m is the measurement matrix and n isin cn is the gaussian noise we develop a cramer rao bound on the mean squared estimation error of the nonzero elements of x corresponding to the genie aided estimator gae which is provided with the locations of the nonzero elements of x intuitively the mean squared estimation error of any estimator without the knowledge of the locations of the nonzero elements of x is no less than that of the gae assuming that l n is fixed we establish the existence of an estimator that asymptotically achieves the cramer rao bound without any knowledge of the locations of the nonzero elements of x as n rarr infin for a a random gaussian matrix whose elements are drawn i i d according to n 0 1

generalizations of convex and related functions abstract the concept of semilocally convexity was recently introduced by ewing 2 this paper defines semilocally quasiconvex semi locally pseudoconvex and other related functions and investigates some of their properties

a trace class operator inequality abstract in this note we generalize the inequality about the trace of positive semidefinite matrix tr a b k tr a k tr b k to hilbert space and obtain a relevant inequality about positive trace class operator

duality in vector optimization via augmented lagrangian abstract this paper is devoted to developing augmented lagrangian duality theory in vector optimization by using the concepts of the supremum and infimum of a set and conjugate duality of a set valued map on the basic of weak efficiency we establish the interchange rules for a set valued map and propose an augmented lagrangian function for a vector optimization problem with set valued data under this augmented lagrangian weak and strong duality results are given then we derive sufficient conditions for penalty representations of the primal problem the obtained results extend the corresponding theorems existing in scalar optimization

online kernel based classification using adaptive projection algorithms the goal of this paper is to derive a novel online algorithm for classification in reproducing kernel hilbert spaces rkhs by exploiting projection based adaptive filtering tools the paper brings powerful convex analytic and set theoretic estimation arguments in machine learning by revisiting the standard kernel based classification as the problem of finding a point which belongs to a closed halfspace a special closed convex set in an rkhs in this way classification in an online setting where data arrive sequentially is viewed as the problem of finding a point classifier in the nonempty intersection of an infinite sequence of closed halfspaces in the rkhs convex analysis is also used to introduce sparsification arguments in the design by imposing an additional simple convex constraint on the norm of the classifier an algorithmic solution to the resulting optimization problem where new convex constraints are added every time instant is given by the recently introduced adaptive projected subgradient method apsm which generalizes a number of well known projection based adaptive filtering algorithms such as the classical normalized least mean squares nlms and the affine projection algorithm apa under mild conditions the generated sequence of estimates enjoys monotone approximation strong convergence asymptotic optimality and a characterization of the limit point further we show that the additional convex constraint on the norm of the classifier naturally leads to an online sparsification of the resulting kernel series expansion we validate the proposed design by considering the adaptive equalization problem of a nonlinear channel and by comparing it with classical as well as with recently developed stochastic gradient descent techniques

kolmogorov equations in infinite dimensions well posedness and regularity of solutions with applications to stochastic generalized burgers equations we develop a new method to uniquely solve a large class of heat equations so called kolmogorov equations in infinitely many variables the equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper lyapunov type functions this way for the first time the solutions are constructed everywhere without exceptional sets for equations with possibly nonlocally lipschitz drifts apart from general analytic interest the main motivation is to apply this to uniquely solve martingale problems in the sense of stroock varadhan given by stochastic partial differential equations from hydrodynamics such as the stochastic navier stokes equations in this paper this is done in the case of the stochastic generalized burgers equation uniqueness is shown in the sense of markov flows

on efficiency and duality for multiobjective programs abstract for a multiobjective nonlinear program which involved inequality and equality constraints wolfe mond weir and general mond weir type duals are formulated and the concept of efficiency pareto optimum is used to state some duality results under generalized f convexity assumptions

online hyperparameter free sparse estimation method in this paper we derive an online estimator for sparse parameter vectors which unlike the lasso approach does not require the tuning of any hyperparameters the algorithm is based on a covariance matching approach and is equivalent to a weighted version of the square root lasso the computational complexity of the estimator is of the same order as that of the online versions of regularized least squares rls and lasso we provide a numerical comparison with feasible and infeasible implementations of the lasso and rls to illustrate the advantage of the proposed online hyperparameter free estimator

vector maximisation and lagrange multipliers the lagrangean function for scalar constrained optimisation problems is extended in a directly analogous manner to constrained vector optimisation problems some simple saddle point results are presented for vector maxima sets conditions are given for the characterisation of the vector maximum set of the original vector problem in terms of the vector maximum sets with respect to the vector lagrangeans

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

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

conjugate duality in set valued vector optimization abstract in this paper conjugate duality results for convexlike set valued vector optimization problems are presented under closedness or boundedness hypotheses some properties of the value mapping of a set valued vector optimization problem are studied a conjugate duality result is also proved for a convex set valued vector optimization problem without the requirements of closedness and boundedness

on matrix trace inequalities and related topics for products of hermitian matrices abstract alternative proofs of some simple matrix trace inequalities of bellman in general inequalities 2 proceedings 2nd international conference on general inequalities e f beckenbach ed pp 89 90 birkhauser basel 1980 neudecker j math anal appl 166 1992 302 303 and yang j math anal appl 133 1988 573 574 are considered and further properties of products of hermitian and positive semi definite matrices are investigated

adaptive constrained learning in reproducing kernel hilbert spaces the robust beamforming case this paper establishes a new paradigm for convexly constrained adaptive learning in reproducing kernel hilbert spaces rkhs although the technique is of a general nature we present it in the context of the beamforming problem a priori knowledge like beampattern specifications and constraints concerning robustness against steering vector errors takes the form of multiple closed convex sets in a high possibly infinite dimensional rkhs every robustness constraint is shown to be equivalent to a min max optimization task formed by means of the robust statistics epsiv insensitive loss function such a multiplicity of specifications turns out to obtain a simple expression by using the rich frame of fixed point sets of certain mappings defined in a hilbert space moreover the cost function that the final solution has to optimize is expressed as an infinite sequence of convex nondifferentiable loss functions springing from the sequence of the incoming training data a novel adaptive beamforming design of linear complexity with respect to the number of unknown parameters to such a constrained nonlinear learning problem is derived by employing a very recently developed version of the adaptive projected subgradient method apsm the method produces a sequence that under mild conditions exhibits properties like the strong convergence to a beamformer that satisfies all of the imposed constraints and in the meantime asymptotically minimizes the sequence of the loss functions imposed by the training data the numerical examples demonstrate that the proposed method displays increased resolution in cases where the classical linear beamforming solutions collapse moreover it leads to solutions which are in agreement with the imposed a priori knowledge as opposed to unconstrained online kernel regression techniques

lexicographical order and duality in multiobjective programming abstract this paper studies the applications of lexicographical order relation for vectors in the mathematical theory of multiobjective programming we show that any pareto minimum of an unconstrained convex problem is the lexicographical minimum for the problem associated to a matrix multiplier having lexicographical positive columns a similar result is also obtained for inequality constrained problems our approach to the theory of duality follows the pattern of jahn 3 but we substitute vectors by matrices in the formulation of the dual problem and the usual scalar order relation by the lexicographical order relation this allows us to state the strong duality theorem in terms of pareto minima and to eliminate some regularity assumptions

duality and saddle point type optimality for generalized nonlinear fractional programming in this paper we establish two theorems of alternative with generalized subconvexlikeness we introduce two dual models for a generalized fractional programming problem theorems of alternative are then applied to establish duality theorems and a saddle point type optimality condition

vector continuous time programming without differentiability in this work continuous time programming problems of vector optimization are considered firstly a nonconvex generalized gordan s transposition theorem is obtained then the relationship with the associated weighting scalar problem is studied and saddle point optimality results are established a scalar dual problem is introduced and duality theorems are given no differentiability assumption is imposed

duality in vector optimization in this paper the problem dual to a convex vector optimization problem is defined under suitable assumptions a weak strong and strict converse duality theorem are proved in the case of linear mappings the formulation of the dual is refined such that well known dual problems of gale kuhn and tucker 8 and isermann 12 are generalized by this approach

an η approximation method in nonlinear vector optimization abstract in this paper a new approach for a solution of a nonlinear multiobjective programming problem is introduced an equivalent approximated vector optimization problem is constructed by a modification of the objective and the constraint functions in the original multiobjective programming problem the connection between weak efficient points in the original multiobjective programming problem and its equivalent approximated vector optimization problem is proved in this way optimality conditions for nonlinear constrained multiobjective programming problems having invex and or generalized invex objective and constraint functions with respect to the same functions are obtained

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

conjugate duality in vector optimization in this paper we develop a conjugate duality theory in vector optimiza tion conjugate duality was fully developed in scalar optimization by rockafellar 3 and provides a unified framework for the duality theory the author and sawaragi extended it to the case of multiobjective optimization by introducing some new concepts such as conjugate maps and subgradients for vector valued set valued maps 4 6 their results are based on the efficiency pareto maximality kawasaki refined their results and obtained a reciprocal duality by introducing the concept of supremum set in an extended euclidean space 1 2 his supremum is based on the weak efficiency weak pareto maximality of the closure of a set in an extended sense the author s newly defined the supremum of a set in the extended multi dimensional euclidean space on the basis of weak ehiciency through several discussions on supremum the definition satisfies some desirable fundamental properties it can be extended to the case of general partially ordered linear topological spaces in a straightforward manner based on this definition of supremum some useful concepts such as conjugate maps and subgradients are introduced for vector valued set valued maps in this paper these concepts enable us to develop the conjugate duality in vector optimization although the results obtained are quite similar to the earlier works by the author and sawaragi 4 or kawasaki 2 our new approach makes the proofs much easier and more understandable and provides a better version of conjugate duality

a duality theorem in multiobjective nonlinear programming we give a duality theorem in multiobjective nonlinear programming problems by means of conjugate set valued functions which were introduced in kawasaki h 1981 conjugate relations and weak subdifferentials of relations math oper res 6 593 607 the duality theorem is reflexive in the sense analogous to ekeland i r temam 1976 convex analysis and variational problems north holland amsterdam

conjugate relations and weak subdifferentials of relations the duality theory for convex programs is based on a concept conjugate of functions and the set of solutions is characterized by subdifferential of a function the purpose of this paper is to extend the concepts conjugate and subdifferential to those of set valued functions relations and to investigate their properties

convex composite multi objective nonsmooth programming this paper examines nonsmooth constrained multi objective optimization problems where the objective function and the constraints are compositions of convex functions and locally lipschitz and g teaux differentiable functions lagrangian necessary conditions and new sufficient optimality conditions for efficient and properly efficient solutions are presented multi objective duality results are given for convex composite problems which are not necessarily convex programming problems applications of the results to new and some special classes of nonlinear programming problems are discussed a scalarization result and a characterization of the set of all properly efficient solutions for convex composite problems are also discussed under appropriate conditions

a characterization of weakly efficient points in this paper we study a characterization of weakly efficient solutions of multiobjective optimization problems mops we find that under some quasiconvex conditions of the objective functions in a convex set of constraints weakly efficient solutions of an mop can be characterized as an optimal solution to a scalar constraint problem in which one of the objectives is optimized and the remaining objectives are set up as constraints this characterization is much less restrictive than those found in the literature up to now

dirichlet operators via stochastic analysis abstract we give sufficient conditions for essential self adjointness of symmetric differential operators dirichlet operators associated with classical dirichlet forms given by probability measures on hilbert spaces under an additional assumption of log concavity for the measures we prove the existence of a gap at the lower end of spectrum of the dirichlet operator and the ergodicity of the corresponding semi group we consider also applications to the study of stochastic dynamics in some classical lattice systems

duality in nondifferentiable vector programming in this paper we study the saddle point optimality conditions and lagrange duality in multiobjective optimization for generalized subconvex like functions we obtain results which will allow us to characterize the solutions for multiobjective programming problems from the saddle point conditions and allow us to relate them to the dual problem solutions which will be adequately defined we also define a new dual problem for the multiobjective programming problem with the special property of being a scalar programming problem

global properties of generalized ornstein uhlenbeck operators on lp rn rn with more than linearly growing coefficients we show that the realization ap of the elliptic operator au div q u f u vu in lp rn rn p 1 generates a strongly continuous semigroup and we determine its domain d ap u w2 p rn rn f u vu lp rn rn if 1 p the diffusion coefficients q qij are uniformly elliptic and bounded together with their first order derivatives the drift coefficients f can grow as x log x and v can grow logarithmically our approach relies on the monniaux pruss theorem on the sum of noncommuting operators we also prove lp lq estimates and under somewhat stronger assumptions we establish pointwise gradient estimates and smoothing of the semigroup in the spaces w p rn rn 0 1 where 1 p

sensitivity analysis for convex multiobjective programming in abstract spaces the main object of this paper is to prove that for a linear or convex multiobjective program a dual program can be obtained which gives the primal sensitivity without any special hypothesis about the way of choosing the optimal solution in the efficient set

semistrictly preinvex functions a new class of functions termed semistrictly preinvex functions is introduced in this paper some properties of semistrictly preinvex functions are discussed in particular the relationship between semistrictly preinvex functions and preinvex functions is investigated some characterization properties of semistrictly preinvex functions are derived under a lower semicontinuous condition and a gradient property of semistrictly preinvex functions is obtained

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

a weak to strong convergence principle for feje monotone methods in hilbert spaces we consider a wide class of iterative methods arising in numerical mathematics and optimization that are known to converge only weakly exploiting an idea originally proposed by haugazeau we present a simple modification of these methods that makes them strongly convergent without additional assumptions several applications are discussed

d invexity and optimality conditions abstract in this paper a generalization of convexity called d invexity is introduced substituting d invex for convex we get some optimality conditions for nondifferentiable multiobjective programming the application is demonstrated by an example

bf l _1 constrained normalized lms algorithms for adaptive beamforming we detail in this paper an l 1 norm linearly constrained normalized least mean square l 1 cnlms algorithm and its weighted version l 1 wcnlms applied to solve problems whose solutions have some degree of sparsity such as the beamforming problem in uniform linear arrays standard hexagonal arrays and non standard hexagonal antenna arrays in addition to the linear constraints present in the cnlms algorithm the l 1 wcnlms and the l 1 cnlms algorithms take into account an l 1 norm penalty on the filter coefficients which results in sparse solutions producing thinned arrays the effectiveness of both algorithms is demonstrated via computer simulations when employing these algorithms to antenna array problems the resulting effect due to the l 1 norm constraint is perceived as a large aperture array with few active elements although this work focuses the algorithm on antenna array synthesis its application is not limited to them i e the l 1 cnlms is suitable to solve other problems like sparse system identification and signal reconstruction where the weighted version the l 1 wcnlms algorithm presents superior performance compared to the l 1 cnlms algorithm

on properties of preinvex functions abstract we consider in this paper the class of preinvex functions introduced by t weir and co workers 1988 j math anal appl 136 29 38 1988 bull austral math soc 38 177 189 under semi continuity conditions a determination of the satisfaction of preinvexity for a function can be achieved via an intermediate point preinvexity check a characterization of a preinvex function in terms of its relationship with an intermediate point preinvexity and prequasi invexity is provided