mixed type converse duality in multiobjective programming problems in this paper we use the fritz john necessary optimality conditions to establish some results on the mixed type converse duality for a class of multiobjective programming problems

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

saddle points criteria in nondifferentiable multiobjective programming with v invex functions via an η approximation method the h approximation method is used to a characterization of solvability of nonconvex nondifferentiable multiobjective programming problems a family of h approximated vector optimization problems is constructed in this approach for the original nondifferentiable multiobjective programming problem the definitions of a vector valued h lagrange function and of an h saddle point for this family of h approximated vector optimization problems are introduced thus the equivalence between a weak pareto optimum of the original multiobjective programming problems and an h saddle point of the h lagrange function in its associated h approximated vector optimization problems is established under v invexity

some nondifferentiable multiobjective programming under generalized d v type i univexity in this paper we introduce new classes of functions called d v type i univex by extending the definition of d v type i functions and consider a multiobjective optimization problem involving generalized d v type i univex functions a number of karush kuhn tucker type sufficient optimality conditions are obtained for a feasible solution to be a weak pareto efficient solution the mond weir type duality results are also presented the results obtained in this paper generalize and extend the previously known result in this area

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

studies in numerical nonlinear instability ii a new look at u t uu x 0 abstract it is shown that in general leap frog schemes any particular unstable solution behaves as an attractor of other solutions for a leap frog discretization of u t uu x 0 a particular kind of unstable solution is constructed which generically attracts any other solution estimates of the overflow time are presented and related to the notions of stability threshold and restricted stability

invex equilibrium problems in this paper we introduce a new class of equilibrium problems known as invex equilibrium problems in the setting of invexity this class of equilibrium problems includes equilibrium problems variational inequalities and variational like inequalities as special cases we use the auxiliary principle technique to suggest and analyze some iterative schemes for solving invex equilibrium problems and study the convergence criteria of these methods under some mild conditions we also consider the concept of well posedness for invex equilibrium problems our results represent significant and important refinements of the previously known results

existence results for semilinear differential equations with nonlocal and impulsive conditions abstract this paper is concerned with the existence for impulsive semilinear differential equations with nonlocal conditions using the techniques of approximate solutions and fixed point existence results are obtained for mild solutions when the impulsive functions are only continuous and the nonlocal item is lipschitz in the space of piecewise continuous functions is not lipschitz and not compact is continuous in the space of bochner integrable functions respectively

characterization of vector strict global minimizers of order 2 in differentiable vector optimization problems under a new approximation method abstract in this paper a new approximation method is introduced to characterize a so called vector strict global minimizer of order 2 for a class of nonlinear differentiable multiobjective programming problems with f convex functions of order 2 in this method an equivalent vector optimization problem is constructed by a modification of both the objectives and the constraint functions in the original multiobjective programming problem at the given feasible point in order to prove the equivalence between the original multiobjective programming problem and its associated f approximated vector optimization problem the suitable f convexity of order 2 assumption is imposed on the functions constituting the considered vector optimization problem

nonlinear stability and convergence of finite difference methods for the good boussinesq equation the good boussinesq equationu tt u xxxx u xx u 2 xx has recently been found to possess an interesting soliton interaction mechanism in this paper we study the nonlinear stability and the convergence of some simple finite difference schemes for the numerical solution of problems involving the good boussinesq equation numerical experimentas are also reported

saddle point criteria for multi dimensional control optimisation problem involving first order pde constraints in this paper the multi dimensional control optimisation problem involving first order pde constraints is considered the absolute value penalty function method is used to solve the considered pro

generalized mixed quasi variational like inequalities in this paper we use the auxiliary principle technique to suggest and analyze some iterative methods for solving generalized mixed quasi variational like inequalities we show that the convergence of the proposed method requires either pseudomonotonicity or partially relaxed strongly monotonicity under some mild condition as special cases one can obtain a number of new and known algorithms for solving variational inequalities and complementarity problems our results represent significant and important refinements of the previously known results

efficiency through variational like inequalities with lipschitz functions in this work first we introduce several notions of invexity and pseudoinvexity for a locally lipschitz function by means of the generalized jacobian we study relationships between these concepts in particular the implications between preinvexity and invexity next we obtain necessary and sufficient optimality conditions for efficient and weak efficient solutions of finite dimensional non necessarily pareto vector optimization problems with locally lipschitz objective functions through solutions of vector variational like inequality problems these conditions are stated via the generalized jacobian and under pseudoinvexity hypotheses and they show that a vector optimization problem can be reformulated as a vector variational like inequality problem this work extends and improves several previous papers where the objective function of the vector optimization problem is assumed to be differentiable or being locally lipschitz the authors consider the componentwise subdifferential based on the clarke s generalized gradients of the components of the objective function throughout the paper some simple examples are given in order to illustrate the main concepts and results

on the relationships between g preinvex functions and semistrictly g preinvex functions a new class of functions termed semistrictly g preinvex functions is introduced in this paper the relationships between semistrictly g preinvex functions and g preinvex functions are investigated under mild assumptions our results improve and extend the existing ones in the literature

the sugeno integral with respect to α preinvex functions abstract in this paper we establish the left hand side of the hermite hadamard inequality for preinvex functions and illustrate that the hermite hadamard inequality for preinvex functions is not valid for the sugeno integral moreover we give several upper bounds for the sugeno integral related to preinvex functions some examples are also provided to show the validity of our results

on optimality conditions for multiobjective optimization problems in topological vector space abstract in this paper we are concerned with a differentiable multiobjective programming problem in topological vector spaces an alternative theorem for generalized k subconvexlike mappings is given this permits the establishment of optimality conditions in this context several generalized fritz john conditions in line to those in hu and ling y hu c ling the generalized optimality conditions of multiobjective programming problem in topological vector space j math anal appl 290 2004 363 372 are obtained and in the presence of the generalized slater s constraint qualification the karush kuhn tucker necessary optimality conditions

ϵ pareto optimality for nondifferentiable multiobjective programming via penalty function abstract necessary and sufficient conditions without a constraint qualification for pareto optimality of multiobjective programming are derived the necessary kuhn tucker condition suggests the establishment of a wolf type duality theorem for nondifferentiable convex multiobjective minimization problems the generalized saddle point for pareto optimality of the vector lagrangian is studied

some relations between variational like inequality problems and vectorial optimization problems in banach spaces in this work we will establish some relations between variational like inequality problems and vectorial optimization problems in banach spaces under invexity hypotheses this paper extends the earlier work of ruiz garzon et al g ruiz garzon r osuna gomez a rufian lizana relationships between vector variational like inequality and optimization problems european j oper res 157 2004 113 119

some nondifferentiable multiobjective programming problems in this paper it is shown that a relaxation defining the class of generalized d v type i functions leads to a new class of multi objective problems which preserves the sufficient optimality and duality results in the scalar non differentiable case and avoids the major difficulty of verifying that the inequality holds for the same kernel function the results obtained in this paper generalize and extend the previously known results in this area

hemiequilibrium like problems abstract in this paper we introduce and consider a new class of equilibrium problems known as hemiequilibrium like problems this new class includes hemiequilibrium equilibrium like problems and several classes of variational inequalities as special cases a number of iterative methods for solving hemiequilibrium like problems are suggested and analyzed by using the auxiliary principle technique we also study the convergence analysis of these iterative methods under some mild conditions the results obtained in this paper can be considered as a novel application of the auxiliary principle technique

some characterizations of strongly preinvex functions in this paper a new class of generalized convex function is introduced which is called the strongly preinvex function we study some properties of strongly preinvex function in particular we establish the equivalence among the strongly preinvex functions strongly invex functions and strongly monotonicity under some suitable conditions as special cases one can obtain several new and previously known results for preinvex invex functions

on minimax fractional optimality conditions with invexity abstract under different forms of invexity conditions sufficient kuhn tucker conditions and three dual models are presented for the minimax fractional programming

an efficient adaptive mesh redistribution method for a non linear dirac equation this paper presents an efficient adaptive mesh redistribution method to solve a non linear dirac nld equation our algorithm is formed by three parts the nld evolution the iterative mesh redistribution of the coarse mesh and the local uniform refinement of the final coarse mesh at each time level the equidistribution principle is first employed to iteratively redistribute coarse mesh points and the scalar monitor function is subsequently interpolated on the coarse mesh in order to do one new iteration and improve the grid adaptivity after an adaptive coarse mesh is generated ideally and finally each coarse mesh interval is equally divided into some fine cells to give an adaptive fine mesh of the physical domain and then the solution vector is remapped on the resulting new fine mesh by an affine method the nld equation is finally solved by using a high resolution shock capturing method on the fixed non uniform fine mesh extensive numerical experiments demonstrate that the proposed adaptive mesh method gives the third order rate of convergence and yields an efficient and fast nld solver that tracks and resolves both small local and large solution gradients automatically

analytical and numerical aspects of certain nonlinear evolution equations ii numerical nonlinear schrodinger equation abstract various numerical methods are employed in order to approximate the nonlinear schrodinger equation namely i the classical explicit method ii hopscotch method iii implicit explicit method iv crank nicolson implicit scheme v the ablowitz ladik scheme vi the split step fourier method f tappert and vii pseudospectral fourier method fornberg and whitham comparisons between the ablowitz ladik scheme which was developed using notions of the inverse scattering transform and the other utilized schemes are obtained

existence of nondensely defined evolution equations with nonlocal conditions abstract this paper is concerned with the existence for nondensely defined evolution equations with nonlocal conditions using the techniques of fixed point theory and approximate solutions existence results are obtained for integral solutions when the nonlocal item is lipschitz continuous or continuous respectively examples are also given to illustrate our results

hemivariational like inequalities in this paper we introduce and consider a new class of variational inequalities known as the hemivariational like inequalities it is shown that the hemivariational like inequalities include hemivariational inequalities variational like inequalities and the classical variational inequalities as special cases the auxiliary principle is used to suggest and analyze some iterative methods for solving hemivariational like inequalities under mild conditions the results obtained in this paper can be considered as a novel application of the auxiliary principle technique

a general equivalence theorem in the theory of discretization methods the lax richtmyer theorem is extended to work in the framework of stetter s theory of discretizations the new result applies to both initial and boundary value problems discretized by finite elements finite differences etc several examples are given together with a comparison with other available equivalence theorems the proof relies on a generalized banach steinhaus theorem 1 introduction in this paper we extend the classical lax richtmyer equivalence theorem 6 so as to cover in a simple way not only initial value problems but also boundary value problems mixed problems etc our theory relies on a generalized banach steinhaus theorem 9 and works essentially in the framework of stetter 13 this set up employs restriction operators to compare the true and discretized solutions as distinct to those theories which use prolongation operators one of the oldest prolongation theories is probably that of aubin summarized in 16 our main result is given in section 2 sections 3 and 4 are devoted to examples and counterexamples the former are meant to show the scope of our result and include the galerkin method for boundary value elliptic problems and semidiscrete and fully discrete schemes for initial value problems the counterexamples prove that the present hypotheses cannot be dispensed with in particular we show that a method which is consistent and convergent for all data in a banach space may be unstable the final section contains a comparison with other available equivalence theorems

a characterization of pseudoinvexity for the efficiency in non differentiable multiobjective problems duality abstract we prove that in order for the kuhn tucker or fritz john points to be efficient solutions it is necessary and sufficient that the non differentiable multiobjective problem functions belong to new classes of functions that we introduce here kt pseudoinvex ii or fj pseudoinvex ii respectively we illustrate it by examples these characterizations generalize recent results given for the differentiable case we study the dual problem and establish weak strong and converse duality results

numerical methods based on additive splittings for hyperbolic partial differential equations we derive and analyze several methods for systems of hyperbolic equations with wide ranges of signal speeds these techniques are also useful for problems whose coefficients have large mean values about which they oscillate with small amplitude our methods are based on additive splittings of the operators into components that can be approximated independently on the different time scales some of which are sometimes treated exactly the efficiency of the splitting methods is seen to depend on the error incurred in splitting the exact solution operator this is analyzed and a technique is discussed for reducing this error through a simple change of variables a procedure for generating the appropriate boundary data for the intermediate solutions is also presented

fixed b subsampling and the block bootstrap improved confidence sets based on p value calibration summary subsampling and block based bootstrap methods have been used in a wide range of inference problems for time series to accommodate the dependence these resampling methods involve a bandwidth parameter such as the subsampling window width and block size in the block based bootstrap in empirical work using different bandwidth parameters could lead to different inference results but traditional first order asymptotic theory does not capture the choice of the bandwidth we propose to adopt the fixed b approach as advocated by kiefer and vogelsang in the heteroscedasticity auto correlation robust testing context to account for the influence of the bandwidth on inference under the fixed b asymptotic framework we derive the asymptotic null distribution of the p values for subsampling and the moving block bootstrap and further propose a calibration of the traditional small b based confidence intervals regions or bands and tests our treatment is fairly general as it includes both finite dimensional parameters and infinite dimensional parameters such as the marginal distribution function simulation results show that the fixed b approach is more accurate than the traditional small b approach in terms of approximating the finite sample distribution and that the calibrated confidence sets tend to have smaller coverage errors than the uncalibrated counterparts

split step methods for the solution of the nonlinear schro dinger equation a split step method is used to discretize the time variable for the numerical solution of the nonlinear schrodinger equation the space variable is discretized by means of a finite difference and a fourier method these methods are analyzed with respect to various physical properties represented in the nls in particular it is shown how a conservation law dispersion and instability are reflected in the numerical schemes analytical and numerical instabilities of wave train solutions are identified and conditions which avoid the latter are derived these results are demonstrated by numerical examples

diagnostic checking in multivariate arma models with dependent errors using normalized residual autocorrelations in this paper we derive the asymptotic distribution of normalized residual empirical autocovariances and autocorrelations under weak assumptions on the noise we propose new portmanteau statistics

the exponential accuracy of fourier and chebyshev differencing methods it is shown that when differencing analytic functions using the pseudospectral fourier or chebyshev methods the error committed decays to zero at an exponential rate

on multisymplecticity of sinc gauss legendre collocation discretizations for some hamiltonian pdes abstract in this paper a new multisymplectic scheme based on sinc collocation discretization in space and gauss legendre collocation discretization in time for some hamiltonian pdes is developed the scheme preserves the multisymplectic geometry structure exactly by satisfying the discrete multisymplectic conservation law moreover the discrete energy and momentum conservative properties of the multisymplectic integrator are also discussed in order to testify the superiority of the multisymplectic method it is applied to nonlinear dirac equation numerical experiments are given to illustrate the accuracy of the approximation and the conserved quantities

methods for the numerical solution of the nonlinear schroedinger equation optimal l2 rates of convergence are established for several fully discrete schemes for the numerical solution of the nonlinear schroedinger equation both finite differences and finite elements are considered for the discretization in space while the integration in time is treated either by the leap frog technique or by a modified crank nicolson procedure which generalizes the one suggested by delfour fortin and payne and possesses two useful conserved quantities

multi symplectic runge kutta methods for nonlinear dirac equations in this paper we consider the multi symplectic runge kutta msrk methods applied to the nonlinear dirac equation in relativistic quantum physics based on a discovery of the multi symplecticity of the equation in particular the conservation of energy momentum and charge under msrk discretizations is investigated by means of numerical experiments and numerical comparisons with non msrk methods numerical experiments presented reveal that msrk methods applied to the nonlinear dirac equation preserve exactly conservation laws of charge and momentum and conserve the energy conservation in the corresponding numerical accuracy to the method utilized it is verified numerically that msrk methods are stable and convergent with respect to the conservation laws of energy momentum and charge and msrk methods preserve not only the inner geometric structure of the equation but also some crucial conservative properties in quantum physics a remarkable advantage of msrk methods applied to the nonlinear dirac equation is the precise preservation of charge conservation law

pseudo invexity and duality in nonlinear programming abstract the purpose of this paper is to study various duality results in nonlinear programming for pseudo invex functions such results were known in the literature for invex functions

g pre invex functions in mathematical programming in the present paper we introduce the concept of g pre invex functions with respect to h defined on an invex set with respect to h these function unify the concepts of nondifferentiable convexity pre invexity and r pre invexity furthermore relationships of g pre invex functions to various introduced earlier pre invexity concepts are also discussed some geometric properties of this class of functions are also derived finally optimality results are established for optimization problems under appropriate g pre invexity conditions

some results on mathematical programming with generalized ratio invexity in this paper a generalized ratio invexity concept has been applied for single objective fractional programming problems a concept which has been invoked seems to be more general than the one used earlier by khan and hanson in such contexts further duality results for fractional programs have also been obtained

an easily implementable fourth order method for the time integration of wave problems abstract we are concerned with the time integration of systems of ordinary differential equations arising from the space discretization of partial differential wave equations with smooth solutions a method is suggested that while being as easily implementable as the standard implicit mid point rule is fourth order accurate the new method is symplectic so that it is very well suited for long time integrations of problems with a hamiltonian structure numerical experiments are reported that refer to a fourth order galerkin space discretization of the korteweg de vries equation and to a pseudospectral space discretization of the same equation

numerical methods for nonlinear dirac equation abstract this paper presents a review of the current state of the art of numerical methods for nonlinear dirac nld equation several methods are extendedly proposed for the 1 1 dimensional nld equation with the scalar and vector self interaction and analyzed in the way of the accuracy and the time reversibility as well as the conservation of the discrete charge energy and linear momentum those methods are the crank nicolson cn schemes the linearized cn schemes the odd even hopscotch scheme the leapfrog scheme a semi implicit finite difference scheme and the exponential operator splitting os schemes the nonlinear subproblems resulted from the os schemes are analytically solved by fully exploiting the local conservation laws of the nld equation the effectiveness of the various numerical methods with special focus on the error growth and the computational cost is illustrated on two numerical experiments compared to two high order accurate runge kutta discontinuous galerkin methods theoretical and numerical comparisons show that the high order accurate os schemes may compete well with other numerical schemes discussed here in terms of the accuracy and the efficiency a fourth order accurate os scheme is further applied to investigating the interaction dynamics of the nld solitary waves under the scalar and vector self interaction the results show that the interaction dynamics of two nld solitary waves depend on the exponent power of the self interaction in the nld equation collapse happens after collision of two equal one humped nld solitary waves under the cubic vector self interaction in contrast to no collapse scattering for corresponding quadric case

pseudospectral method for the good boussinesq equation we prove the nonlinear stability and convergence of a fully discrete pseudospectral scheme for the good boussinesq equation utt uxxxx uxx u2 xx numerical comparisons with finite difference schemes are also reported

on the existence and asymptotic behaviour of solutions of an evolution equation and an application to the feynman kac theorem abstract in this paper we study the existence of mild solutions of a semilinear evolution equation on an unbounded interval the rapidity of the growth of those solutions is characterized moreover we investigate the local and global attractivity of solutions of an equation in question and we describe their asymptotic behaviour our investigations are conducted in a real separable banach space

pseudoinvexity optimality conditions and efficiency in multiobjective problems duality abstract in this paper we establish characterizations for efficient solutions to multiobjective programming problems which generalize the characterization of established results for optimal solutions to scalar programming problems so we prove that in order for kuhn tucker points to be efficient solutions it is necessary and sufficient that the multiobjective problem functions belong to a new class of functions which we introduce similarly we obtain characterizations for efficient solutions by using fritz john optimality conditions some examples are proposed to illustrate these classes of functions and optimality results we study the dual problem and establish weak strong and converse duality results

studies in numerical nonlinear instability iii augmented hamiltonian systems leap frog explicit mid point discretizations of hamiltonian systems are considered it is proved that the discrete evolution preserves the symplectic structure of the phase space the kolmogorov arnold moser kam theory is applied to guarantee the boundedness of the computed points under suitable restrictions of the time step the general ideas introduced are employed to provide an extensive analysis of the leap frog discretization of the complex equation iz t z 2 z 0 which describes the nonlinear selfinteraction of a fourier mode the paper emphasizes the relations between numerical analysis and classical mechanics dynamical systems

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

proper efficiency in nonconvex vector maximization problems abstract vector maximization problems arise when more than one objective function are to be simultaneously maximized over a feasibility region the concept of proper efficiency has been introduced by geoffrion in order to eliminate points of a certain anomalous type in this paper a generalization is provided for the characterization of the properly efficient solutions as solutions of some parametric programming problems a specific characterization is given in the case of bicriterion programs

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

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

nondifferentiable multiobjective programming under generalized di invexity abstract in this paper we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints we introduce new concepts of d i invexity and generalized d i invexity in which each component of the objective and constraint functions is directionally differentiable in its own direction d i new fritz john type necessary and karush kuhn tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be weakly efficient efficient or properly efficient moreover we prove weak strong converse and strict duality results for a mond weir type dual under various types of generalized d i invexity assumptions

optimality and duality for generalized fractional programming involving nonsmooth f ρ convex functions using a parametric approach we establish necessary and sufficient conditions and derive duality theorems for a class of nonsmooth generalized minimax fractional programming problems containing f r convex functions

d ρ η θ invexity in multiobjective optimization abstract in this paper a generalization of convexity is considered in the case of multiobjective optimization problems where the functions involved are non differentiable under d invexity assumptions on the functions involved weak strong and converse duality results are proved to relate weak pareto efficient solutions of the multiobjective programming problems pvp dvp and mwd we have also established the karush kuhn tucker sufficient optimality condition

duality theorems of vector valued n set functions abstract the wolfe and mond weir types of dual problems for convex vector valued n set functions are formulated and we prove the weak duality duality and converse duality theorems for these types of problems

nondifferentiable multiobjective programming under generalized d univexity abstract in this paper we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints we introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex strong pseudoinvex weak quasi invex weak pseudoinvex and strong quasi invex functions in aghezzaf and hachimi numer funct anal optim 22 2001 775 d invex functions in antczak europ j oper res 137 2002 28 and univex functions in bector et al univex functions and univex nonlinear programming proc admin sci assoc canada 1992 p 115 by utilizing the new concepts we derive a karush kuhn tucker sufficient optimality condition and establish mond weir type and general mond weir type duality results for the nondifferentiable multiobjective programming problem

the vector exact l1 penalty method for nondifferentiable convex multiobjective programming problems abstract in this paper the vector exact l 1 penalty function method for nondifferentiable convex multiobjective programming problems is analyzed the vector penalized optimization problem with the vector exact l 1 penalty function is defined conditions are given guaranteeing the equivalence of the sets of weak pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penealized optimization problem with the vector exact l 1 penalty function this equivalence is established for nondifferentiable vector optimization problems with convex functions

on sufficiency and duality for nonsmooth multiobjective programming problems involving generalized v r invex functions abstract in this paper a class of nonsmooth multiobjective programming problems with inequality constraints is considered we introduce the concepts of v r pseudo invex strictly v r pseudo invex and v r quasi invex functions in which the involved functions are locally lipschitz based upon these generalized v r invex functions sufficient optimality conditions for a feasible point to be an efficient or a weakly efficient solution are derived appropriate duality theorems are proved for a mond weir type dual program of a nonsmooth multiobjective programming under the aforesaid functions

impulsive problems for semilinear differential equations with nonlocal conditions abstract this paper is concerned with the existence of impulsive semilinear differential equations with nonlocal conditions using the technique of fixed point theory existence results are obtained for mild solutions when the nonlocal item is lipschitz is not lipschitz and not compact respectively

optimality conditions for a nonconvex set valued optimization problem in this paper we study necessary and sufficient optimality conditions for a set valued optimization problem convexity of the multifunction and the domain is not required a definition of k approximating multifunction is introduced this multifunction is the differentiability notion applied to the problem a characterization of weak minimizers is obtained for invex and generalized k convexlike multifunctions using the lagrange multiplier rule

multiobjective programming under d invexity abstract in this paper a generalization of convexity is considered in the case of nonlinear multiobjective programming problem where the functions involved are nondifferentiable by considering the concept of pareto optimal solution and substituting d invexity for convexity the fritz john type and karush kuhn tucker type necessary optimality conditions and duality in the sense of mond weir and wolfe for nondifferentiable multiobjective programming are given

the multi symplecticity of partitioned runge kutta methods for hamiltonian pdes in this article we consider partitioned runge kutta prk methods for hamiltonian partial differential equations pdes and present some sufficient conditions for multi symplecticity of prk methods of hamiltonian pdes

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

minimax fractional programming under nonsmooth generalized f ρ θ d univexity abstract in this paper we are concerned with a nondifferentiable minimax fractional problem with inequality constraints we introduce a new class of generalized convex function that is nonsmooth generalized f d univex function in the framework of the new concept we derive kuhn tucker type sufficient optimality conditions and establish weak strong and converse duality theorems for the problem and its three different types of dual problems

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

split step spectral schemes for nonlinear dirac systems abstract the paper considers split step spectral schemes for the numerical integration of nonlinear dirac systems in 1 1 dimensions proofs of stability and convergence are given along with numerical experiments which clearly show the superiority of the suggested methods over standard and split step finite difference algorithms

the numerical study of a nonlinear one dimensional dirac equation we study the convergence of a difference scheme for a nonlinear one dimensional dirac equation also we show some numerical experiments by using this scheme

proper efficiency conditions and duality results for nonsmooth vector optimization in banach spaces under φ ρ invexity abstract in this paper a new class of nonsmooth nonconvex multiobjective programming problems in banach spaces is considered the sufficient optimality conditions for efficiency and proper efficiency are established under nonsmooth invexity and generalized invexity notions after extending these concepts to the functions between banach spaces further mond weir duality theorems are also established under invexity for the considered vector optimization problems in banach spaces

second order duality for the variational problems under ρ η θ invexity in this paper we introduce the concept of second order duality for the variational problems using r h q invexity type conditions weak strong and converse duality results of mangasarian and mond weir type of variational problems are established under r h q invexity assumptions many examples and counterexamples are illustrated to justify our work

on strongly α preinvex functions in this paper by means of a series of counterexamples we study in a systematic way the relationships among pseudo quasi preinvexity strict strong pseudo quasi invexity and strict strong pseudo quasi monotonicity results obtained in this paper can be viewed as a refinement and improvement of the results of noor and noor m a noor k i noor some characterizations of strongly preinvex functions j math anal appl 316 2006 697 706

optimality conditions and duality for nondifferentiable multiobjective programming problems involving d r type i functions in this paper new classes of nondifferentiable functions constituting multiobjective programming problems are introduced namely the classes of d r type i objective and constraint functions and moreover the various classes of generalized d r type i objective and constraint functions are defined for directionally differentiable multiobjective programming problems sufficient optimality conditions and various mond weir duality results are proved for nondifferentiable multiobjective programming problems involving functions of such type finally it is showed that the introduced d r type i notion with r 0 is not a sufficient condition for wolfe weak duality to hold these results are illustrated in the paper by suitable examples

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