the primal dual active set strategy as a semismooth newton method this paper addresses complementarity problems motivated by constrained optimal control problems it is shown that the primal dual active set strategy which is known to be extremely efficient for this class of problems and a specific semismooth newton method lead to identical algorithms the notion of slant differentiability is recalled and it is argued that the max function is slantly differentiable in lp spaces when appropriately combined with a two norm concept this leads to new local convergence results of the primal dual active set strategy global unconditional convergence results are obtained by means of appropriate merit functions

complementarity framework for non linear dynamic analysis of skeletal structures with softening plastic hinges in this paper we describe an algorithm for the incremental state update of elasto plastic systems with softening the algorithm uses a complementary pivoting technique and is based on casting the incremental state update as a complementarity problem in developing the algorithm we take advantage of the special features of solid and structural mechanics problems to achieve good computational performance and hence the ability to compute numerical solutions to practical size problems for example the notion of a tangent stiffness matrix arises numerical examples using models of skeletal structures are presented to demonstrate the practicability of the algorithm the numerical examples also raise some interesting questions about multiplicity of the solutions copyright 2010 john wiley sons ltd

introduction to the concept of recursiveness of fuzzy functions abstract the main aim of this paper is to extend church s soft thesis to fuzzy calculus let w 0 1 be an ordered semiring the fuzzy functions are considered as associating an output to an input with membership degree belonging to w for such w functions the concepts of crisp computability and recursiveness are extended obtaining the so called w computability and w recursiveness respectively a few properties of w recursive functions are analized and the equivalence between w recursive and w computable functions is shown

infinitely distributive t norms on complete lattices and pseudo complements in this paper we have introduced the concepts of t prime element t prime radical element and t semi prime element and have studied their properties we have investigated the construction methods of new infinitely distributive t norms from given infinitely distributive t norms by means of t prime elements and pseudo complements if every element of l is t prime radical element then we show that l is a complete brouwerian lattice and email protected if l is an algebraic lattice t is a t norm on l and every compact element of l is idempotent then we obtain that email protected we show that l r is a complete lattice and that the restriction of t to l r is an infinitely distributive t norm on l r when t is an infinitely distributive t norm on l and 0 is a t prime we present infinitely distributive t norms on a complete sublattice l and study their properties

mesh adaptive computation of upper and lower bounds in limit analysis summary an efficient procedure to compute strict upper and lower bounds for the exact collapse multiplier in limit analysis is presented with a formulation that explicitly considers the exact convex yield condition the approach consists of two main steps first the continuous problem under the form of the static principle of limit analysis is discretized twice one per bound using particularly chosen finite element spaces for the stresses and velocities that guarantee the attainment of an upper or a lower bound the second step consists of solving the resulting discrete non linear optimization problems these are reformulated as second order cone programs which allows for the use of primal dual interior point methods that optimally exploit the convexity and duality properties of the limit analysis model to benefit from the fact that collapse mechanisms are typically highly localized a novel method for adaptive meshing is introduced the method first decomposes the total bound gap as the sum of positive contributions from each element in the mesh and then refines those elements with higher contributions the efficiency of the methodology is illustrated with applications in plane stress and plane strain problems copyright q 2008 john wiley sons ltd

upper and lower bounds in limit analysis adaptive meshing strategies and discontinuous loading summary upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimisation problems the membership constraints for von mises and mohrcoulomb plasticity criteria are written as a set of quadratic constraints which permits to solve the optimisation problem using specific algorithms for second order conic program socp from the stress field at the lower bound and the velocities at the upper bound we construct a novel error estimate based on elemental and edge contributions to the bound gap these contributions are employed in an adaptive remeshing strategy that is able to reproduce fan type mesh patterns around points with discontinuous surface loading the solution of this type of problems is analysed in detail and from this study some additional meshing strategies are also described we particularise the resulting formulation and strategies to two dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature copyright c 2007 john wiley sons ltd

a projected newton algorithm for the dual convex program of elastoplasticity summary in this paper we study a dual optimization problem that arises when taking a mathematical programming approach to incremental state update in nonlinear problems the mathematical programming approach stems from energy based descriptions of constitutive models we describe a projected newton algorithm to solve the dual optimization problem this algorithm requires solution of an unconstrained optimization problem at the integration point level rather than a constrained one as carried out by classical return mapping schemes especially implementation of multi surface plasticity models is no more involved than that of single surface models we explore characteristics and performance of the projected newton algorithm through numerical examples insights gained from such a further exploration of mathematical programming algorithms are likely to aid in development of successive convex programming approaches to geometric nonlinear and other non convex problems such as non associated flow models copyright 2014 john wiley sons ltd

the theory of approximate prices analytical foundations of experimental cost benefit analysis in a fuzzy decision space abstract the essay presents a theory of efficient prices for cost benefit analysis in a fuzzy space the approach proceeds by taking consumers income and producers outputs and costs as given the price preferences of consumers and producers are elicited and then embedded in a fuzzy space through fuzzy mappings to obtain a fuzzy compact price space where fuzzy price decisions are constructed solutions to the fuzzy price decision problems are abstracted through fuzzy mathematical programming to obtain fuzzy equilibrium prices from the fuzzy price space measures of price disagreement fuzzy consumer surplus and fuzzy producer surplus are advanced theorems of existence and uniqueness are stated the total result is a theory of fuzzy prices for cost benefit analysis for decision problem in general including cases where market imputations of prices may not be available to us as well as those cases where market failure may yield price distortions the theory is not only compactible with either contigent variation method direct information elicitation and revealed preference method market based evaluation but provides a direction for cases where problems may exist in both a computational example is provided to illustrate the working mechanism of the theory

distributive n ary semicopulas on lattices in the present paper definitions of an n ary semicopula on a bounded lattice l a distributive n ary semicopula on l and an infinite distributive n ary semicopula on l are introduced a relation between the set of all bounded lattices l with a distributive n ary semicopula on l and the set of all bounded lattices l with a distributive m ary semicopula on l where 2 n 2 m n m is obtained the method is given for investigation of the following questions a description of all bounded lattices l such that every n ary semicopula on l is distributive and a description of all complete lattices l such that every n ary semicopula on l is infinite distributive

a fuzzy decision theory of optimal social discount rate collective choice theoretic abstract in this essay we present a fuzzy decision theory of the optimal social discount rate by combining methods of fuzzy logic consensus combination of expert judgments and fuzzy aggregation algorithms are developed for computing optimal social discount rates from individual and collective time preferences the results are examined against the computation of social discount rate on individual preferences as measured by utilities an example is provided to illustrate the applicational mechanism of the theory the essay is concluded with an appendix which is devoted to examining the properties of the required time set for the construction of the social discount

a new approach to fuzzy programming abstract a fuzzy program is defined in the usual way as a sequence of statements instruction which are considered as functions possibly fuzzy functions and fuzzy predicates defined on the given input domain the essential difference in the approach presented in this paper is the new interpretation of the execution of fuzzy programs and a new method of evaluating fuzzy predicates the result of the fuzzy program execution is an appropriate fuzzy subset in the output domain

a note on upper bound formulations in limit analysis summary in this paper we study some recent formulations for the computation of upper bounds in limit analysis we show that a previous formulation presented by the authors does not guarantee the strictness of the upper bound nor does it provide a velocity field that satisfies the normality rule everywhere we show that these deficiencies are related to the quadrature employed for the evaluation of the dissipation power we derive a formulation that furnishes a strict upper bound of the load factor which in fact coincides with a formulation reported in the literature from the analysis of these formulations we propose a post process which consists in computing exactly the dissipation power for the optimum upper bound velocity field this post process may further reduce the strict upper bound of the load factor in particular situations finally we also determine the quadratures that must be used in the elemental and edge gap contributions so that they are always positive and their addition equals the global bound gap copyright 2012 john wiley sons ltd

a fuzzy language abstract with the aim of designing and implementing programming languages that take into account the fuzzy paradigm we will modify the classical lambda calculus by adding a degree to each term and by redefining the b reduction thus for the new calculus to verify the church rosser property the degree computed with can be made through a function that is a t norm or an s conorm with this new tool we design a nondeterminist language that satisfies fuzzy data programming requirements and an example of its behaviour is shown

the arnold winther mixed fem in linear elasticity part i implementation and numerical verification abstract following some de rham complex arnold and winther have recently proposed a symmetric mixed finite element method mfem in linear elasticity this paper describes the implementation of the symmetric mfem and its 30 30 local stress stiffness matrices and studies the implementation of the lowest order scheme for general boundary conditions numerical experiments in model examples in computational mechanics illustrate the robust locking free convergence behavior and support the theoretically predicted experimental convergence rates

an adaptive multi scale approach to the modelling of masonry structures we present an adaptive multi scale approach for predicting the mechanical behaviour of masonry structures modelled as dynamic frictional multi body contact problems in this approach the iterative splitting of the contact problem into normal contact and frictional contact is combined with a semismooth newton primal dual active set procedure to calculate deformations and openings in the model structures this algorithm is then coupled with a novel adaptive multi scale technique involving a macroscopic scale which is the size of the masonry structure and a mesoscopic scale which is the size of the constituents bricks stone blocks to predict appearance of dislocations and stress distribution in large scale masonry structures comparisons of the numerical results with data from experimental tests and from practical observations illustrate the predictive capability of the multi scale algorithm

applications of fuzzy set theory to mathematical programming mathematical programming is one of the areas to which fuzzy set theory has been applied extensively primarily based on bellman and zadeh s model of decision in fuzzy environments models have been suggested which allow flexibility in constraints and fuzziness in the objective function in traditional linear and nonlinear programming in integer and fractional programming and in dynamic programming these models in turn have been used to offer computationally efficient approaches for solving vector maximum problems this paper surveys major models and theories in this area and offers some indication on future developments which can be expected

two families of fuzzy integrals abstract in this paper we present two definitions of fuzzy integrals arising from the t seminorm and the t semiconorm concepts we show that sugeno s fuzzy integral is a particular case of them and we study their principal properties finally we suggest some applications of these results

chance constrained programming with fuzzy parameters this paper extends chance constrained programming from stochastic to fuzzy environments analogous to stochastic programming some crisp equivalents of chance constraints in fuzzy environments are presented we also propose a technique of fuzzy simulation for the chance constraints which are usually hard to be converted to their crisp equivalents finally a fuzzy simulation based genetic algorithm is designed for solving this kind of problems and some numerical examples are discussed

a new approach to uncertain parameter linear programming abstract a novel method for solving uncertain linear programming is put forward in this paper in contrast to stochastic linear programming and most fuzzy linear programming models the parameters of the problem discussed here are neither random variables with known probability distributions nor fuzzy parameters with known possibility distributions all we know about the parameters is merely their intervals of existence to solve this kind of uncertain linear programming might be very attractive since many actual decision problems could be formulated as such if we do not have enough information about the parameters in this paper the concept of a confidence function for inequalities is introduced based on this definition the problem is solved by an iterative algorithm then the convergence of the algorithm is proved and the decision risk grades for different confidence functions are discussed finally an illustrative example is given to demonstrate the actual application of thismethod

pseudo t norms and implication operators direct products and direct product decompositions in this paper we further study the pseudo t norms and implication operators on a complete brouwerian lattice and discuss their direct products and direct product decompositions

mixed finite elements for elasticity there have been many efforts dating back four decades to develop stable mixed finite elements for the stress displacement formulation of the plane elasticity system this requires the development of a compatible pair of finite element spaces one to discretize the space of symmetric tensors in which the stress field is sought and one to discretize the space of vector fields in which the displacement is sought although there are number of well known mixed finite element pairs known for the analogous problem involving vector fields and scalar fields the symmetry of the stress field is a substantial additional difficulty and the elements presented here are the first ones using polynomial shape functions which are known to be stable we present a family of such pairs of finite element spaces one for each polynomial degree beginning with degree two for the stress and degree one for the displacement and show stability and optimal order approximation we also analyze some obstructions to the construction of such finite element spaces which account for the paucity of elements available

a finite element procedure for rigorous numerical enclosures on the limit load in the analysis of multibody structures a rigorous finite element numerical procedure is proposed for the computation of guaranteed lower and upper bounds for the limit load of failure in a system of linear elastic blocks in mutual non penetrative contact with given friction first the static and kinematic principles are formulated as continuous optimization problems and existence of a solution to the corresponding limit load problems at the infinite dimensional level is established two numerical approaches are devised one for each limit load problem to obtain actual numerical bounds on the unique critical load the first approach uses the static limit load problem involving stresses in conjunction with a non standard conforming finite element method to obtain a linear program from which one can derive a lower safe bound for the limit load and an expression for the corresponding stress field the second approach uses the kinematic limit load problem to obtain a linear optimization problem from which one can determine an upper unsafe bound for the limit load and an expression for the failure mode together these procedures give rise to rigorous numerical enclosures on the limit load

a note on chance constrained programming with fuzzy coefficients this paper deals with nonlinear chance constrained programming as well as multiobjective case and goal programming with fuzzy coefficients occurring in not only constraints but also objectives we also present a fuzzy simulation technique for handling fuzzy objective constraints and fuzzy goal constraints finally a fuzzy simulation based genetic algorithm is employed to solve a numerical example