imprecise weights in weber facility location problem abstract this paper presents a method for locating multiple facilities on a plane bounded by a convex polygon under the criterion minimize the sum of all the transportation cost where the cost per unit distances are known imprecisely assuming some fuzzy aspiration levels for each of the goals and basing these on a comparison of flat fuzzy numbers the original fuzzy problem is transferred into a crisp satisfactory model to determine a suitable solution we will maximize the minimum of the surpluses over the aspiration levels rectilinear distance norm has been taken as the scenario and may be considered as in an urban setting this induces the problem with a non linear objective function which is equivalent to a linear program a numerical example has been given to illustrate the solution procedure

fuzzy logic based algorithms for maximum covering location problems this paper concerns a class of maximum covering location problems in networks in uncertain environments it is assumed that a relative weights of demand nodes are either deterministic or imprecise described by linguistic expressions and b potential facility site locations are limited to network nodes the concept of coverage is extended to include a degree of node coverage which means that the borders between the subset of covered demand nodes and the subset of uncovered demand nodes are inexact the acceptable service distance travelling times from a facility site to demand nodes are modelled by fuzzy sets three new algorithms for choosing the best facility locations are developed which assume that 1 demands at all nodes are equally important 2 relative weights of demand at nodes are deterministic and 3 weights of demand at nodes are imprecise and described by linguistic terms respectively the algorithms are based on searching among potential facility nodes by applying comparison operations on discrete fuzzy sets it is shown how to extend the proposed algorithms from one site to multi site covering problems illustrative examples of selecting locations for logistics centres in a distribution company are given

a discrete location model with fuzzy accessibility measures abstract in crisply defined discrete location problems a number of facilities are to be located at specific points within an area according to precisely quantified criteria however in many location problems especially those associated with social policies non crisply defined criteria are used such as how near or accessible a facility is or how important certain issues are etc in these cases a fuzzy sets approach is more appropriate this paper presents an application of the set partitioning set covering with equality constraints type of integer programming formulation to a discrete location problem with fuzzy accessibility criteria the solution method suggested uses the symmetry of the objectives and the constraints introduced by bellman and zadeh

a geometrical theory for spiral waves in excitable media in this paper we develop a geometrical theory for waves in excitable reacting media using singular perturbation arguments and dispersion of traveling plane wave trains we derive an approximate theory of wave front propagation which has strong resemblance to the geometrical diffraction theory of high frequency waves in hyperbolic systems governed by the eikonal equation using this theory we study the effect of curvature on waves in excitable media specifically rotating spiral patterns in planar regions from this theory we are able to determine the frequency and wavelength for spiral patterns in excitable nonoscillatory media

error bounds for piecewise convex quadratic programs and applications in this paper we establish a local error estimate for feasible solutions of a piecewise convex quadratic program and a global error estimate for feasible solutions of a convex piecewise quadratic program these error estimates provide a unified approach for deriving many old and new error estimates for linear programs linear complementarity problems convex quadratic programs and affine variational inequality problems the approach reveals the fact that each error estimate is a consequence of some reformulation of the original problem as a piecewise convex quadratic program or a convex piecewise quadratic program in a sense even robinson s result on the upper lipschitz continuity of a polyhedral mapping can be considered as a special case of error estimates for approximate solutions of a piecewise convex quadratic program as an application we derive new global error estimates for iterates of the proximal point algorithm for solving a convex piecewise quadratic program

two parallel distribution algorithms for convex constrained minimization problems abstract a parallel gradient distribution pgd approach for minimizing a nonsmooth convex function on a block separable convex set x of rn and a parallel variable distribution pvd approach for minimizing a nonsmooth convex function on an inseparable closed convex set x of rn are presented which are constructed by using the moreau yosida regularization of the convex functions the convergence analysis for the two approaches is given as well

ranking the sequences of fuzzy values when ranking fuzzy values there is an ambiguity in selecting the most preferred ranked sequence from a collection of candidate sequences because every sequence has a possibility to which the preference relations in the sequence are correct in this paper we propose a method for ranking the sequences of fuzzy values that assigns a preference degree to each ranked sequence each preference degree indicates the relative preference of the given sequence over the other sequences the proposed method gives information regarding which sequence could be classified as the most preferred sequence and which sequences as alternatives

new improved error bounds for the linear complementarity problem new local and global error bounds are given for both nonmonotone and monotone linear complementarity problems comparisons of various residuals used in these error bounds are given a possible candidate for a best error bound emerges from our comparisons as the sum of two natural residuals

fuzzy location problems on networks location problems concern a wide set of fields where it is usually assumed that exact data are known however in real applications the location of the facility considered can be full of linguistic vagueness that can be appropriately modelled using networks with fuzzy values thus fuzzy location problems on networks arise this paper deals with their general formulation and the description of the ways to solve them namely we show the variety of problems that can be considered in this context and for some of them we propose the most operative approaches for their solution

application of decision analysis techniques to the weber facility location problem a location problem with future uncertainties about the data is considered several possible scenarios about the future values of the parameters are postulated however it is not clear which of these scenarios will actually happen we find the location that will best accommodate the possible scenarios four rules utilized in decision theory are examined the expected value rule the optimistic rule the pessimistic rule and the minimax regret rule the solution for the squared euclidean distance is explicitly found algorithms are suggested for general convex distance metrics an example problem is solved in detail to illustrate the findings and computational experiments with randomly generated problems are reported

a posteriori error bounds for the linearly constrained varitional inequality problem in this paper we derive a posteriori error bound of an approximate solution to a linearly constrained variational inequality problem three measures of error are used with each depending on a particular characterization of an exact solution and related to a certain class of iterative methods

on the robustness of type 1 and interval type 2 fuzzy logic systems in modeling research on the robustness of fuzzy logic systems flss an imperative factor in the design process is very limited in the literature specifically when a system is subjected to small deviations of the sampling points operating points it is of great interest to find the maximum tolerance of the system which we refer to as the system s robustness in this paper we present a methodology for the robustness analysis of interval type 2 flss it2 flss that also holds for t1 flss hence making it more general a procedure for the design of robust it2 flss with a guaranteed performance better than or equal to their t1 counterparts is then proposed several examples are performed to demonstrate the effectiveness of the proposed methodologies it was concluded that both t1 and it2 flss can be designed to achieve robust behavior in various applications and preference one or the other in general is application dependant it2 flss having a more flexible structure than t1 flss exhibited relatively small approximation errors in the several examples investigated the methodologies presented in this paper lay the foundation for the design of flss with robust properties that will be very useful in many practical modeling and control applications

weak sharp minima in mathematical programming the notion of a sharp or strongly unique minimum is extended to include the possibility of a nonunique solution set these minima will be called weak sharp minima conditions necessary for the solution set of a minimization problem to be a set of weak sharp minima are developed in both the unconstrained and constrained cases these conditions are also shown to be sufficient under the appropriate convexity hypotheses the existence of weak sharp minima is characterized in the cases of linear and quadratic convex programming and for the linear complementarity problem in particular a result of mangasarian and meyer is reproduced that shows that the solution set of a linear program is always a set of weak sharp minima whenever it is nonempty consequences for the convergence theory of algorithms are also examined especially conditions yielding finite termination

convex functions with unbounded level sets and applications to duality theory a class of convex functions with unbounded level sets but good behavior at infinity analyse non lineaire gauthier villars paris 1989 pp 101 122 is investigated characterizations and properties are given the results are then applied to studying sequential approximation schemes for optimization problems and to duality theory when the involved functions have unbounded level sets in particular the convergence properties of stationary sequences for the dual of a convex program are studied and methods for associating with it a primal sequence converging to a solution of the primal problem are demonstrated

a condition number for differentiable convex inequalities for a system of differentiable convex inequalities a new bound is given for the absolute error in an infeasible point in terms of the absolute residual by using this bound a condition number is defined for the system of inequalities which gives a bound for the relative error in an infeasible point in terms of the relative residual

numerical methods for interval and fuzzy number comparison based on the probabilistic approach and dempster shafer theory there are many different methods for interval and fuzzy number comparison proposed in the literature which provide the results of comparison in the form of a real or boolean value in this paper we use the dempster shafer theory of evidence with its probabilistic interpretation to justify and construct the method which provides the result of comparison in the form of an interval or fuzzy number the complete and consistent set of expressions for inequality and equality relations between intervals and fuzzy numbers has been obtained in the framework of the probabilistic approach these relations make it possible to compare intervals and fuzzy numbers with real values and may be considered as an asymptotic limit of the results we obtain using the dempster shafer theory a natural fuzzy extension of the proposed approach is considered and discussed using some illustrative examples

existence of approximate exact penalty in constrained optimization in this paper we use the penalty approach in order to study constrained minimization problems in infinite dimensional spaces a penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem in this paper we establish the exact penalty property for a large class of inequality constrained minimization problems

extension of hoffman s error bound to polynomial systems given any linear system defined by linear inequalities equalities in re n hoffman s error bound says that the distance from any point x in re n to the solution set of the linear system is bounded by a constant independent of x times a certain residual function evaluated at x this paper considers arbitrary possibly nonconvex polynomial systems defined by polynomial inequalities equalities it is shown that the solution sets of such systems are in general holder continuous as the right hand side changes in contrast to the lipschitzian continuity for the linear case also for any convex quadratic inequality system possessing an interior solution the authors show that its solution set behaves in a lipschitzian manner as the right hand side varies this result sharpens the earlier error bound results by mangasarian and robinson for general convex differentiable inequality systems which in addition to the interiority assumption require either an asymptotic constraint qualification con

use of v shaped stable patterns to study high negative curvature velocity dependence of an excitable medium abstract constant velocity v shaped patterns are used to investigate experimentally the curvature velocity relation at high negative curvatures for the belousov zhabotinsky reaction in a thin layer it is shown that curvature velocity relation is essentially nonlinear and the linear eikonal equation is correct only if the curvature is sufficiently small the v shaped patterns are proved to be stable under local perturbations results are compared with theoretical predictions based on a kinematic approach showing a good agreement

normal maps inducted by linear transformations we study a certain piecewise linear manifold which we call the normal manifold associated with a polyhedral convex set and a family of continuous functions called normal maps that are induced on this manifold by continuous functions from rn to rn these normal maps occur frequently in optimization and equilibrium problems and the subclass of normal maps induced by linear transformations plays a key role our main result is that the normal map induced by a linear transformation is a lipschitzian homeomorphism if and only if the determinant of the map in each n cell of the normal manifold has the same nonzero sign

a smooth variational principle with applications to hamilton jacobi equations in infinite dimensions abstract we prove that if x is a banach space which admits a smooth lipschitzian bump function then for every lower semicontinuous bounded below function there exists a lipschitzian smooth function g on x such that f g attains its strong minimum on x thus extending a result of borwein and preiss we then show how the above result can be used to obtain existence and uniqueness results of viscosity solutions of hamilton jacobi equations in infinite dimensional banach spaces a without assuming the radon nikodym property

minimization of locally lipschitzian functions this paper presents a globally convergent model algorithm for the minimization of a locally lipschitzian function the algorithm is built on an iteration function of two arguments and the convergence theory is developed parallel to analogous results for the problem of solving systems of locally lipschitzian equations application of the theory to a wide range of nonsmooth optimization problems is discussed these include the minimax problem the composite optimization problem the implicit programming problem and others a recently developed nonmonotone linesearch technique is shown to be applicable in this nonsmooth context and an extension to constrained problems is also presented

minimizing and stationary sequences of constrained optimization problems we study some fundamental asymptotic properties associated with the well posedness of constrained optimization problems emphasis is placed on the relation between minimizing and stationary sequences and their characterizations in terms of a set of asymptotic karush kuhn tucker kkt optimality conditions unlike the subdifferential approach used by auslender cominetti and crouzeix we use a residual function approach that is closely tied to the theory of error bounds this approach handles constraints explicitly and allows the effective treatment of infeasible stationary sequences the asymptotic kkt conditions provide an asymptotic optimality certificate for inequality constrained programs specializations of the results to convex quadratically constrained convex quadratic spline minimization problems and convex programs with holderian minima are discussed an application of the results to the convergence of a family of newton type iterative descent methods involving singular quasi newton matrices for solving a constrained minimization problem is also presented

on lp programming abstract our paper treats the primal and dual program of lp programming lp programming is a generalization of lp approximation problems there is a strict connection between lp programming and geometrical programming because in both of them geometrical inequality plays a fundamental role the structure of our paper follows that of klafszkys 1 in the first sections duality theorems are proved which play an important role in mathematical programming most of these results can be found in petersons and eckers 3 4 5 but our proofs are much more simple and we show these fundamental properties more detailed afterwards the relation between the lagrange function and the optimal solution pair is investigated regularity is investigated as well and we show the marginal value of lp programming in the end linear programming lp constrained lp approximation problems the quadratically constrained quadratic programming and compromise programming are shown as special cases of lp programming

a unified separation theorem for closed sets in a banach space and optimality conditions for vector optimization using the technique of variational analysis and in terms of normal cones we establish unified separation results for finitely many closed not necessarily convex sets in banach spaces which not only cover the existing nonconvex separation results and a classical convex separation theorem but also recapture the approximate projection theorem with help of the separation result for closed sets we provide necessary and sufficient conditions for approximate pareto solutions of constrained vector optimization problems in particular we extend some basic optimality results for approximate solutions of numerical optimization problems to the vector optimization setting

error bounds for nondifferentiable convex inequalities under a strong slater constraint qualification a global error bound is given on the distance between an arbitrary point in then dimensional real spacern and its projection on a nonempty convex set determined bym convex possibly nondifferentiable inequalities the bound is in terms of a natural residual that measures the violations of the inequalities multiplied by a new simple condition constant that embodies a single strong slater constraint qualification cq which implies the ordinary slater cq a very simple bound on the distance to the projection relative to the distance to a point satisfying the ordinary slater cq is given first and then used to derive the principal global error bound

error bounds for lower semicontinuous functions in normed spaces without the convexity or analyticity assumption we study error bounds for an inequality system defined by a general lower semicontinuous function and establish sufficient necessary conditions on the existence of error bounds in infinite dimensional normed spaces some characterizations for a convex inequality system to possess an error bound in a reflexive banach space are also given as applications in dealing with the hoffman error bound result in normed spaces we give a computable lipschitz bound constant which is better than previous lipschitz bound constants in some examples we also consider error bounds for quadratic functions on rn

the gradual covering decay location problem on a network abstract in covering problems it is assumed that there is a critical distance within which the demand point is fully covered while beyond this distance it is not covered at all in this paper we define two distances within the lower distance a demand point is fully covered and beyond the larger distance it is not covered at all for a distance between these two values we assume a gradual coverage decreasing from full coverage at the lower distance to no coverage at the larger distance

on minimizing and critical sequences in nonsmooth optimization let f be a bounded below lower semicontinuous function from a banach space into r cup infty we study the relationships between minimizing and critical sequences of f where the criticality condition is given in terms of some subdifferential partial here the objective function f is not supposed to be convex or smooth our work extends that of auslender and crouzeix and that of chou ng and pang

singular perturbation theory of traveling waves in excitable media a review abstract waves of chemical or electrical activity traveling through space have been observed in several contexts chemical reaction mixtures in non convecting liquid phase cell suspensions nerve axons and neuromuscular tissues typically wave supporting preparations are excitable that is they respond and sensitivity to perturbations are rapidly damped out but suprathreshold disturbances trigger an abrupt and substantial response the abruptness of the response can be exploited by the methods of singular perturbation theory to obtain a mathematical description of wave propagation in spatially distributed excitable media singular perturbation analysis of propagating waves in one spatial dimension is straightforward and uncontentious but the analysis of propagating waves in one spatial dimension is straightforward and several fundamentally different ways we compare and contrast the approaches taken by greenberg zykov fife krinskii and his collaborators and ourselves with particular emphasis on the case of rotating spiral waves our intention is to bring some order to the important but difficult theory of propagating waves in two dimensional excitable media in conclusion we discuss briefly some possible extensions of the singular perturbation approach to propagating wave surfaces in three dimensional space

finite termination of the proximal point algorithm this paper concerns the notion of a sharp minimum on a set and its relationship to the proximal point algorithm we give several equivalent definitions of the property and use the notion to prove finite termination of the proximal point algorithm