a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set abstract in this paper we provide a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function defined on a noncompact set our criterion is based on a new existence level introduced in this paper that describes the behavior of the function as its argument approaches the extended boundary of the minimization domain some examples are included to illustrate the efficiency of our criterion

characterization of a condition related to a class of preinvex functions in the theory of invex functions a very important role is played by the so called condition c we present a convenient characterization of this condition in terms of starlike sets and projections

invex sets and preinvex functions on riemannian manifolds the concept of a geodesic invex subset of a riemannian manifold is introduced geodesic invex and preinvex functions on a geodesic invex set with respect to particular maps are defined the relation between geodesic invexity and preinvexity of functions on manifolds is studied using proximal subdifferential certain results concerning extremum points of a non smooth geodesic preinvex function on a geodesic invex set are obtained the main value inequality and the mean value theorem in invexity analysis are extended to cartan hadamard manifolds

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

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

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

a new method of solving nonlinear mathematical programming problems involving r invex functions a new approach to a solution of a nonlinear constrained mathematical programming problem involving r invex functions with respect to the same function is introduced an approximated problem associated with an original nonlinear mathematical programming problem is presented that involves approximated functions constituting the original problem the equivalence between optima points for the original mathematical programming problem and its approximated optimization problem is established under r invexity assumption

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

new optimality conditions and duality results of g type in differentiable mathematical programming abstract in this paper a new class of differentiable functions called g invex functions with respect to is introduced by extending the definition of invex functions new necessary optimality conditions of g f john and g karush kuhn tucker type are obtained for differentiable constrained mathematical programming problems the g invexity concept introduced is used to prove the sufficiency of these necessary optimality conditions further a so called g mond weir type dual is formulated and various duality results are also established by assuming the functions involved to be g invex with respect to the same function

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

multidimensional sdes with singular drift and universal construction of the polymer measure with white noise potential we study the existence and uniqueness of solution for stochastic differential equations with distributional drift by giving a meaning to the stroock varadhan martingale problem associated to such equations the approach we exploit is the one of paracontrolled distributions introduced in forum math pi 3 2015 e6 as a result we make sense of the three dimensional polymer measure with white noise potential

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

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

solution of the least squares problem for logistic function given the data pi ti fi i 1 m m 3 we consider the best least squares approximation of parameters for the logistic function t f t 1 e t 0 r we give necessary and sufficient conditions which guarantee the existence of such optimal parameters

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

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

relationships between pre invex concepts abstract it is well known that some properties of convex optimization problems especially sufficient conditions for optimality and duality conditions are preserved when convexity is weakened to pre invexity however there are several distinct pre invex concepts b vex b pre invex pre univex p r pre invex and these are not equivalent the pre invexity concepts mentioned above have also some properties which are characteristic and invariant for functions belonging to these classes of functions

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

optimality and duality for nonsmooth multiobjective programming using g type i functions abstract in this paper generalized g type i functions are defined for a nonlinear multiobjective programming problem where the functions involved are assumed to be locally lipschitz this new class of functions is a generalization of g invex functions defined in kang et al 2012 20 examples are given to show the existence of these functions g type kuhn tucker necessary conditions are established for a nondifferentiable multiobjective programming problem gmp by using suitable g type i functions sufficient optimality conditions are derived for the problem gmp further a mond weir type dual gmwd is formulated and using these newly defined functions various duality results are established

hardy littlewood polya type theorems for invex functions in this paper the hardy littlewood polya theorem on majorization is extended from convex functions to invex ones some variants for pseudo invex and quasi invex functions are also considered the framework used is that of similarly separable vectors the results obtained are illustrated for monotonic monotonic in mean and star shaped vectors respectively applications to relative invexity are given

a new exact exponential penalty function method and nonconvex mathematical programming abstract a new exact penalty function method called the l1 exact exponential penalty function method is introduced in this approach the so called the exponential penalized optimization problem with the l1 exact exponential penalty function is associated with the original optimization problem with both inequality and equality constraints the l1 exact exponential penalty function method is used to solve nonconvex mathematical programming problems with r invex functions with respect to the same function the equivalence between sets of optimal solutions of the original mathematical programming problem and of its associated exponential penalized optimization problem is established under suitable r invexity assumption also lower bounds on the penalty parameter are given for which above these values this result is true

a non linear parabolic pde with a distributional coefficient and its applications to stochastic analysis abstract we consider a non linear parabolic partial differential equation pde on r d with a distributional coefficient in the non linear term the distribution is an element of a besov space with negative regularity and the non linearity is of quadratic type in the gradient of the unknown under suitable conditions on the parameters we prove local existence and uniqueness of a mild solution to the pde and investigate properties like continuity with respect to the initial condition and blow up times we prove a global existence and uniqueness result assuming further properties on the non linearity to conclude we consider an application of the pde to stochastic analysis in particular to a class of non linear backward stochastic differential equations with distributional drivers

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

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

the infinitesimal generator of the stochastic burgers equation we develop a martingale approach for a class of singular stochastic pdes of burgers type including fractional and multi component burgers equations by constructing a domain for their infinitesimal generators it was known that the domain must have trivial intersection with the usual cylinder test functions and to overcome this difficulty we import some ideas from paracontrolled distributions to an infinite dimensional setting in order to construct a domain of controlled functions using the new domain we are able to prove existence and uniqueness for the kolmogorov backward equation and the martingale problem we also extend the uniqueness result for energy solutions of the stochastic burgers equation of gubinelli and perkowski j am math soc 31 2 427 471 2018 to a wider class of equations as applications of our approach we prove that the stochastic burgers equation on the torus is exponentially l 2 ergodic and that the stochastic burgers equation on the real line is ergodic

generalized convex fuzzy mappings and fuzzy variational like inequality in this paper we introduce the concepts of some generalized convex fuzzy mappings from r n to the set of fuzzy numbers under the condition of upper or lower semicontinuity a new criterion be obtained for the existence of a fuzzy preinvex mapping a fuzzy preinvex mapping can be achieved when the invex subset of r n satisfies certain conditions the relations between generalized convex fuzzy mappings are discussed and some properties are obtained that relate the concepts of fuzzy pseudoinvex and fuzzy prequasiinvex mapping fuzzy invex and fuzzy preinvex mapping fuzzy preinvex and fuzzy prequasiinvex mapping we also discuss the relationship between the fuzzy variational like inequality the fuzzy weak variational like inequality and fuzzy optimization problems and an application example of a fuzzy variational like inequality the fuzzy variational like inequality representation of a fuzzy transportation equilibrium problem

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

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

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

total least squares fitting michaelis menten enzyme kinetic model function the michaelis menten enzyme kinetic model f x a b ax b x a b 0 is widely used in biochemistry pharmacology biology and medical research given the data p i x i y i i 1 m m 3 we consider the total least squares tls problem for the michaelis menten model we show that it is possible that the tls estimate does not exist as the main result we show that the tls estimate exists if the data satisfy some natural conditions some numerical examples are included

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

nonsmooth minimax programming under locally lipschitz φ ρ invexity abstract minimax programming problems involving locally lipschitz invex functions are considered the parametric and non parametric necessary and sufficient optimality conditions for a class of nonsmooth minimax programming problems are obtained under nondifferentiable invexity assumption imposed on objective and constraint functions when the sufficient conditions are utilized parametric and non parametric dual problems in the sense of mond weir and wolfe may be formulated and duality results are derived for the considered nonsmooth minimax programming problem with the reference to the said functions we extend some results of optimality and duality for a larger class of nonsmooth minimax programming problems

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

on invex sets and preinvex functions abstract in this paper we consider the class of the invex function introduced by hanson we show that under certain condition an invex function defined on an invex set a is preinvex on a similarly a quasiinvex function defined on an invex set a is pre quasiinvex

a littlewood paley description of modelled distributions abstract we exhibit a fundamental link between hairer s theory of regularity structures 11 and the paracontrolled calculus of 9 by using paraproducts we provide a littlewood paley description of the spaces of modelled distributions in regularity structures that is similar to the besov description of classical holder spaces

on ratio invexity in mathematical programming abstract the nonlinear fractional programming problem is considered the functions involved in the objective function and constraints are assumed to be invex and differentiable it is shown that the ratio of invex functions is invex sufficient optimality and duality theorems are presented for an invex fractional programming problem

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

mean value in invexity analysis abstract in this paper a generalization of the mean value theorem is considered in the case of functions defined on an invex set with respect to which is not necessarily connected

on the existence of best mitscherlich verhulst and west growth curves for generalized least squares regression practical difficulties arise in fitting mitscherlich verhulst or west growth curves to data obstacles include divergent iterations negative values for theoretically positive parameters or the absence of any best fitting curve an analysis reveals that such obstacles occur near removable singularities of the objective function to be minimized for the regression such singularities lie at the transition to different types of curves including exponentials hyperbolae lines and step functions removing the singularities fits all such curves into a connected compactified topological space which guarantees the existence of a global minimum for the continuous objective function and which also provides a smooth and transparent transition from one type of curve to another

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