grobner bases via linkage in this paper we give a sufficient condition for a set g of polynomials to be a groebner basis with respect to a given term order for the ideal i that it generates our criterion depends on the linkage pattern of the ideal i and of the ideal generated by the initial terms of the elements of g we then apply this criterion to ideals generated by minors and pfaffians more precisely we consider large families of ideals generated by minors or pfaffians in a matrix or a ladder where the size of the minors or pfaffians is allowed to vary in different regions of the matrix or the ladder we use the sufficient condition that we established to prove that the minors or pfaffians form a reduced groebner basis for the ideal that they generate with respect to any diagonal or anti diagonal term order we also show that the corresponding initial ideal is cohen macaulay our proof relies on known results in liaison theory combined with a simple hilbert function computation in particular our arguments are completely algebraic

nondegenerate solutions and related concepts in affine variational inequalities the notion of a strictly complementary solution for complementarity problems is extended to that of a nondegenerate solution of variational inequalities several equivalent formulations of nondegeneracy are given in the affine case an existence theorem for a nondegenerate solution is given in terms of several related concepts which are shown to be equivalent in this context these include a weak sharp minimum the minimum principle sufficiency and error bounds the gap function associated with the variational inequality plays a central role in this existence theorem

new approximation schemes for general variational inequalities in this paper we suggest and consider a class of new three step approximation schemes for general variational inequalities our results include ishikawa and mann iterations as special cases we also study the convergence criteria of these schemes

mixed quasi variational inequalities in this paper we use the resolvent operator and auxiliary principle techniques to suggest and analyze several iterative algorithms for solving mixed quasi variational inequalities and related problems we study the convergence criteria of these algorithms under mild conditions we also study the global stability and existence of a unique solution of these quasi variational inequalities by using the dynamical systems approach our results represent refinement and improvement of the previously known results for variational inequalities

predictor corrector methods for general mixed quasi variational inequalities in this paper we use the auxiliary principle technique to suggest a class of predictor corrector methods for solving general mixed quasi variational inequalities the convergence of the proposed methods only requires the partially relaxed strongly monotonicity of the operator which is weaker than co coercivity as special cases we obtain various known and new results for solving various classes of variational inequalities and related problems

algorithm for solving a new class of generalized nonlinear implicit quasi variational inclusions in banach spaces abstract in this paper we introduce and study a new class of generalized nonlinear implicit quasi variational inclusions with general h monotone operator in banach spaces by using the proximal mapping and nadler s theorem we suggest and analyze a class of iterative algorithm for solving the generalized nonlinear implicit quasi variational inclusion first an existence theorem of solutions for the generalized nonlinear implicit quasi variational inclusion is proved under suitable assumptions then the convergence of the iterative sequences generated by the new algorithm is proved

on a multicommodity stochastic flow network with unreliable nodes subject to budget constraint from the quality management and decision making view point reliability and unreliability are important indices to measure the quality level for a stochastic flow network in a multicommodity stochastic flow network with unreliable nodes the branches and nodes all have several possible capacities and may fail different types of the commodity which are transmitted through the same network simultaneously compete the capacities of branches and nodes in this paper we first define the system capacity as a vector for a multicommodity stochastic flow network with unreliable nodes then we design a performance index which is the probability that the upper bound of the system capacity is a given pattern subject to the budget constraint it can be applied to evaluate the quality level for such a network a simple approach based on minimal cuts is thus presented to evaluate the performance index

a modified forward backward splitting method for maximal monotone mappings we consider the forward backward splitting method for finding a zero of the sum of two maximal monotone mappings this method is known to converge when the inverse of the forward mapping is strongly monotone we propose a modification to this method in the spirit of the extragradient method for monotone variational inequalities under which the method converges assuming only the forward mapping is lipschitz continuous on some closed convex subset of its domain the modification entails an additional forward step and a projection step at each iteration applications of the modified method to decomposition in convex programming and monotone variational inequalities are discussed

on random variational inequalities abstract in this paper we consider a random variational inequality an existence theorem for a unique solution of a random variational inequality is proved which includes the results of noor lions and stampacchia several special cases which can be obtained from our results are also discussed

sensitivity analysis for abstract equilibrium problems we develop the general framework of sensitivity analysis for equilibrium problems in the setting of vector topological normed space our approach does not make any recourse to geometrical properties and the obtained result can be viewed as an extension and generalization of the well known results on variational inequalities in the literature even though we have worked under arbitrary constraints k with holder property that have been decisive in our treatment we have obtained in a similar spirit of domokos j math anal appl 230 1999 382 389 the best lower bound for the continuity modulus despite of the properties of the boundary of k

gorenstein liaison for toric ideals of graphs abstract a central question in liaison theory asks whether every cohen macaulay graded ideal of a standard graded k algebra belongs to the same g liaison class of a complete intersection in this paper we answer this question positively for toric ideals defining edge subrings of bipartite graphs

stochastic flow networks via multiple paths under time threshold and budget constraint this paper extends the quickest path problem to a stochastic flow network in which the capacity of each arc is variable we mainly evaluate the system reliability that d units of data can be sent from the source to the sink under both time threshold t and budget b in particular the data are transmitted through multiple disjoint minimal paths simultaneously in order to reduce the transmission time a simple algorithm is proposed to generate all lower boundary points for d t b and the system reliability can then be computed in terms of such points by utilizing a union of subsets computational complexity in both worst case and average cases show that the proposed algorithm can be executed efficiently

algorithms for general monotone mixed variational inequalities abstract in this paper we suggest and analyze some new iterative methods for solving general monotone mixed variational inequalities which are being used to study odd order and nonsymmetric boundary value problems arising in pure and applied sciences these new methods can be viewed as generalizations and extensions of the methods of he solodov and tseng and noor for solving monotone mixed variational inequalities

the g biliaison class of symmetric determinantal schemes we consider a family of schemes that are defined by minors of a homogeneous symmetric matrix with polynomial entries we assume that they have maximal possible codimension given the size of the matrix and of the minors that define them we show that these schemes are g bilinked to a linear variety of the same dimension in particular they can be obtained from a linear variety by a finite sequence of ascending g biliaisons on some determinantal schemes we describe the biliaisons explicitly in the proof of theorem 2 3 in particular it follows that these schemes are glicci

some applications of variational inequalities in nonsmooth analysis abstract in this paper we apply some results on variational inequalities to the clarke generalized gradient and the generalized second order directional derivative f x u v and obtain some variational inequalities of them

internet packet routing application of a k quickest path algorithm this paper describes a study on the application of an algorithm to rank the k quickest paths to the routing of data packets in internet networks for this purpose an experimental framework was developed by considering two types of random generated networks to simulate values of the ip packet sizes a truncated pareto distribution was defined having in mind to reflect a key feature of internet traffic namely its self similar stochastic nature results concerning the average cpu times of the algorithm for the different sets of experiments will be presented and discussed

tangent projection equations and general variational inequalities in this paper we establish the equivalence between the general variational inequalities and tangent projection equations this equivalence is used to discuss the local convergence analysis of a wide class of iterative methods for solving the general variational inequalities we show that some existing methods can identify the optimal face after finitely many iterations under the degenerate assumption

sensitivity analysis of generalized variational inequalities abstract dafermos studied the sensitivity properties of the solutions of a variational inequality with regard to continuity and differentiability of such solutions with respect to a parameter in the present paper we extend this analysis for a generalized variational inequality of the type introduced by noor of which the variational inequality of dafermos is a particular case our results are such that they automatically extend the regularity properties of solutions with respect to a parameter when the variational inequality is treated on a hilbert space

mixed ladder determinantal varieties abstract we investigate ladder determinantal varieties defined by ideals of minors of possibly different sizes in the different regions the steps of one sided ladders l these varieties are an important generalization of the classical ladder determinantal varieties i e with equal size minors since they are very closely related to schubert varieties this being the first main result of this paper we show that they correspond to opposite cells in schubert varieties in flag varieties of type a n in consequence one deduces the normality and the cohen macaulayness of these one sided ladder determinantal varieties with ideals of mixed size minors as well as the fact that they have rational singularities next we show that up to products by affine spaces each of these varieties is a basic open set in a classical ladder determinantal variety i e with equal size minors and that it contains as a basic open set another classical ladder determinantal variety this result along with a general localisation lemma used to show it enables us to compute the divisor class group and singular locus of the coordinate rings of these varieties as well as to determine when they are gorenstein

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

on a class of variational inequalities in this paper we introduce and study a new unified and general class of variational inequalities we derive the general error estimates for the finite element solutions of variational inequalities it has been shown that a class of contact problems with friction terms arising in elastostatics can be studied in the framework of variational inequalities several special cases which can be obtained from the general results are also discussed

on the identification of active constraints nondegeneracy conditions that guarantee that the optimal active constraints are identified in a finite number of iterations are studied results of this type have only been established for a few algorithms and then under restrictive hypothesis the main result is a characterization of those algorithms that identify the optimal constraints in a finite number of iterations this result is obtained with a nondegeneracy assumption which is equivalent in the standard nonlinear programming problem to the assumption that there is a set of strictly complementary lagrange multipliers as an important consequence of the authors results the way that this characterization applies to gradient projection and sequential quadratic programming algorithms is shown

g biliaison of ladder pfaffian varieties the ideals generated by pfaffians of mixed size contained in a subladder of a skew symmetric matrix of indeterminates define arithmetically cohen macaulay projectively normal reduced and irreducible projective varieties we show that these varieties belong to the g biliaison class of a complete intersection in particular they are glicci