on integration of fuzzy mappings abstract in this paper we introduce the concept of an integral of a fuzzy mapping this generalises the integral introduced by matloka 10 and also extends riemann stieltjes integral over a closed interval to fuzzy mappings

limited memory bfgs systems with diagonal updates abstract in this paper we investigate a formula to solve systems of the form b i x y where b is a limited memory bfgs quasi newton matrix and is a positive constant these types of systems arise naturally in large scale optimization such as trust region methods as well as doubly augmented lagrangian methods we show that provided a simple condition holds on b 0 and the system b i x y can be solved via a recursion formula that requires only vector inner products this formula has complexity m 2 n where m is the number of l bfgs updates and n m is the dimension of x

a note of rsu integrals of fuzzy valued functions abstract in this paper we define rsu integral of compact fuzzy valued functions directly and show that this definition is stronger than the definition introduced by wu cong fuzzy sets and systems 84 1996 301 308 by means of the rsu integral of interval valued functions in addition we generalize the integral existence theorem of wu cong

on affine scaling algorithms for nonconvex quadratic programming we investigate the use of interior algorithms especially the affine scaling algorithm to solve nonconvex indefinite or negative definite quadratic programming qp problems although the nonconvex qp with a polytope constraint is a hard problem we show that the problem with an ellipsoidal constraint is easy when the hard qp is solved by successively solving the easy qp the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions

an approximation scheme for distributionally robust nonlinear optimization we consider distributionally robust optimization problems drops with nonlinear and nonconcave dependence on uncertain parameters the drop can be written as a nonsmooth nonlinear program with a

harmonic finite element analysis for anisotropic viscoelasticity a numerical methodology for predicting the linear anisotropic viscoelastic behavior of bodies that can be uniquely described in cylindrical coordinates is devised the methodology is an extension of the fourier finite element method and is based on a combination of finite element discretization in the radial and longitudinal directions and fourier decomposition in the angular direction the proposed method is capable of handling inhomogeneous polar orthotropic viscoelastic material properties in general the method provides dimensional reduction in the finite element formulation which leads to a reduction in the complexity of the numerical model including the meshing process overall the method is shown to be competent mainly because of the efficient exploitation of the angular description of the geometry and the properties distribution a numerical example is given for the analysis of an orthotropic viscoelastic ring under asymmetric shear loading

on a subproblem of trust region algorithms for constrained optimization we study a subproblem that arises in some trust region algorithms for equality constrained optimization it is the minimization of a general quadratic function with two special quadratic constraints properties of such subproblems are given it is proved that the hessian of the lagrangian has at most one negative eigenvalue and an example is presented to show that the hessian may have a negative eigenvalue when one constraint is inactive at the solution

bases of fuzzy algebraic substructures abstract an axiomatic approach is developed concerning the existence of a basis for certain fuzzy algebraic substructures let the set of truth values be a complete brouwerian lattice l let g be an abelian group we show that there exists an l subgroup of g which does not have a p basis even if g is finite let f be a field of characteristic p 0 and let a b be l subfields of f such that a b we show there exists an intermediate l subfield of a b which does not have a relative p basis over b even if f has finite relative imperfection degree over the support of b when l 0 1 we show that every fuzzy subgroup of g with the sup property has a p basis and that every intermediate fuzzy subfield of a b with the sup property has a relative p basis if certain compatibility conditions hold

harmonic variables a new approach to nonlinear periodic problems abstract the paper presents a new method of formulating and solving nonlinear periodic problems the method is based on harmonic representation of each variable and explicit definitions of operations between these variables the definition also includes analytical functions the method is especially suitable for implrmentation in computer codes the use of the method reduces and simplifies the analytical and programming efforts associated with the solution of nonlinear periodic problems in addition the method makes it possible to obtain solutions with high harmonic resolution without any additional effort

rsu integral of interval valued functions and fuzzy valued functions redefined abstract in this paper we prove that the rsu integral of constant interval valued functions does not exist according to the definition of 6 and we give a generalized definition of rsu integral of interval valued functions and fuzzy valued functions and the integrability of constant interval valued functions in the sense of new definition the generalized rsu integral keeps the properties of 6 and especially we obtain the linearity of integral which also improves the corresponding result in the sense of 6

analysis of a quadratic programming decomposition algorithm we analyze a decomposition algorithm for minimizing a quadratic objective function separable in mathbf x 1 and mathbf x 2 subject to the constraint that mathbf x 1 and mathbf x 2 are orthogonal vectors on the unit sphere our algorithm consists of a local step where we minimize the objective function in either variable separately while enforcing the constraints followed by a global step where we minimize over a subspace generated by solutions to the local subproblems we establish a local convergence result when the global minimizers are nondegenerate our analysis employs necessary and sufficient conditions and continuity properties for a global optimum of a quadratic objective function subject to a sphere constraint and a linear constraint the analysis is connected with a new domain decomposition algorithm for electronic structure calculations

quasi newton trust region algorithm for non smooth least squares problems1this work was supported by cnpq of brazil and the national natural science foundation of china 1 in this paper we present a quasi newton trust region algorithm for non smooth least squares problems which possess the smooth plus non smooth decomposition this method uses a smooth subproblem with second order information to approximate the locally lipschitzian function which is important to increase the convergence rate of the algorithm and deal with the large residual non smooth least squares problems the global and superlinear convergence of this algorithm are established

an extension of karmarkar projective algorithm for convex quadratic programming we present an extension of karmarkar s linear programming algorithm for solving a more general group of optimization problems convex quadratic programs this extension is based on the iterated application of the objective augmentation and the projective transformation followed by optimization over an inscribing ellipsoid centered at the current solution it creates a sequence of interior feasible points that converge to the optimal feasible solution in o ln iterations each iteration can be computed in o ln3 arithmetic operations wheren is the number of variables andl is the number of bits in the input in this paper we emphasize its convergence property practical efficiency and relation to the ellipsoid method

newton s method with a model trust region modification a modified newton method for unconstrained minimization is presented and analyzed the modification is based upon the model trust region approach this report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified newton iteration several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis very strong convergence results are presented concerning the minimization algorithm in particular the explicit use of second order information is justified by demonstrating that the iterates converge to a point which satisfies the second order necessary conditions for minimization with the exception of very pathological cases this occurs whenever the algorithm is applied to problems with continuous second partial derivatives

on rsu integral of interval valued functions and fuzzy valued functions abstract in this paper we define and discuss the rsu integral of interval valued functions and fuzzy valued functions

spectral element fourier method for transitional flows in complex geometries an efficient spectral element fourier method is presented for the direct numerical simulation of transitional internal flows in complex geometries this method is applied for the spatial discretization of the unsteady incompressible three dimensional navier stokes equations in the velocity pressure formulation the resulting discrete equations are solved by a semi implicit method in time where the nonlinear convective term is treated explicitly direct numerical simulations are performed to investigate the spatial structure and temporal evolution of two and three dimensional transitional flows in grooved channels

duality and sensitivity in nonconvex quadratic optimization over an ellipsoid abstract in this paper a duality framework is discussed for the problem of optimizing a nonconvex quadratic function over an ellipsoid additional insight is obtained from the observation that this nonconvex problem is in a sense equivalent to a convex problem of the same type from which known necessary and sufficient conditions for optimality readily follow based on the duality results some existing solution procedures are interpreted as in fact solving the dual the duality relations are also shown to provide a natural framework for sensitivity analysis

variational analysis of an extended eigenvalue problem abstract for a symmetric matrix b rn n and a vector a rn the maximal extended eigenvalue a max x r n s t b i x a x t x 1 is known to arise in optimality conditions for the mathematical programming problemp a given by max x t b x 2 a t x x t x 1 as well as in extended rayleigh ritz type results pertaining to the one parameter family of nonsymmetric border perturbations ofb given by a t a b a t a t nonsmooth analysis is employed in order to describe the function with special emphasis on its sensitivity near the origin further connections with p a are drawn

a simple duality proof in convex quadratic programming with a quadratic constraint and some applications abstract in this paper a simple derivation of duality is presented for convex quadratic programs with a convex quadratic constraint this problem arises in a number of applications including trust region subproblems of nonlinear programming regularized solution of ill posed least squares problems and ridge regression problems in statistical analysis in general the dual problem is a concave maximization problem with a linear equality constraint we apply the duality result to 1 the trust region subproblem 2 the smoothing of empirical functions and 3 to piecewise quadratic trust region subproblems arising in nonlinear robust huber m estimation problems in statistics the results are obtained from a straightforward application of lagrange duality

some notes on the supremum and infimum of the set of fuzzy numbers abstract in this paper we give a necessary and sufficient condition under which a pair of usual functions of on 0 1 supn un supn un can be determined a fuzzy number and give a condition under which the supremum and infimum for a sequence of fuzzy numbers preserve the approximation properties for a metric d in addition we obtain the criterion that the continuous fuzzy valued function on a closed interval can attain its supremum and infimum

line integral alternating minimization algorithm for dual energy x ray ct image reconstruction we propose a new algorithm called line integral alternating minimization liam for dual energy x ray ct image reconstruction instead of obtaining component images by minimizing the discrepancy between the data and the mean estimates liam allows for a tunable discrepancy between the basis material projections and the basis sinograms a parameter is introduced that controls the size of this discrepancy and with this parameter the new algorithm can continuously go from a two step approach to the joint estimation approach liam alternates between iteratively updating the line integrals of the component images and reconstruction of the component images using an image iterative deblurring algorithm an edge preserving penalty function can be incorporated in the iterative deblurring step to decrease the roughness in component images images from both simulated and experimentally acquired sinograms from a clinical scanner were reconstructed by liam while varying the regularization parameters to identify good choices the results from the dual energy alternating minimization algorithm applied to the same data were used for comparison using a small fraction of the computation time of dual energy alternating minimization liam achieves better accuracy of the component images in the presence of poisson noise for simulated data reconstruction and achieves the same level of accuracy for real data reconstruction

elimination of gibbs phenomena from error analysis of finite element results a change of variables is presented that improves the accuracy of fourier half range sine series used in numerical harmonic analysis the change in variables results in an interpolation formula that passes through the endpoints of tabulated data

an approach to identification for robust control given measured data generated by a discrete time linear system we propose a model consisting of a linear time invariant system affected by norm bounded perturbation under mild assumptions the plants belonging to the resulting uncertain family form a convex set the approach depends on two key parameters an a priori given bound of the perturbation and the input used to generate the data it turns out that the size of the uncertain family can be reduced by intersecting the model families obtained by making use of different inputs the model validation problem in this identification scheme is analyzed for a given energy level the invalidation problem yields the family of those models which can never be invalidated for any possible input of fixed energy and any possible perturbation this leads to the intersection of all uncertain families a consequence of the invalidation problem is that for finite length measurements not all models can be invalidated using fixed energy inputs

a finite element spectral method with application to the thermoelastic analysis of space structures a combined spectral finite element method is devised for use in finding the thermal and thermoelastic dynamic response of truss structures to time periodic loading the thermal problem is strongly non linear due to the presence of heat radiation the problems considered are typical in the analysis of space structures in the method proposed the spatial domain is first discretized using a consistent finite element formulation then the resulting semi discrete equations in time are solved analytically by using a spectral method that is symbolically coded some numerical examples are presented which demonstrate the performance of the method and its ability to identify some key characteristics in space structure problems

parallel computing using semianalytical finite element method in this paper a parallel computing technique using a semianalytical finite element method and its implementation method are studied and the speedup in the elapsed computing time is discussed the structural analysis of an axisymmetric body with nonaxisymmetric boundary conditions is considered by using a semianalytical finite element method the displacements and the boundary conditions are expressed by a fourier series by the orthogonality properties of the fourier series the equilibrium equations are fully decoupled for each mode therefore these decoupled equations can be well adapted to the individual processors of a parallel computer two example problems are considered for the verification of the developed code and for the application of the parallel processing to practical problems the computing time by parallel processing is compared with that by sequential processing and a large amount of improvement in the elapsed computing time is achieved by parallel processing from the computational experiments a speedup of 4 6 times in elapsed time is observed with six processors of alliant fx2812 at seoul national university 14 refs

an interior point algorithm to solve computationally difficult set covering problems we present an interior point approach to the zero one integer programming feasibility problem based on the minimization of a nonconvex potential function given a polytope defined by a set of linear inequalities this procedure generates a sequence of strict interior points of this polytope such that each consecutive point reduces the value of the potential function an integer solution not necessarily feasible is generated at each iteration by a rounding scheme the direction used to determine the new iterate is computed by solving a nonconvex quadratic program on an ellipsoid we illustrate the approach by considering a class of difficult set covering problems that arise from computing the 1 width of the incidence matrix of steiner triple systems

an affine scaling reduced preconditional conjugate gradient path method for linear constrained optimization abstract this paper presents an affine scaling reduced preconditional conjugate gradient path approach in association with nonmonotonic interior backtracking line search technique for the linear constrained optimization employing the affine scaling preconditional conjugate gradient to form the curvilinear path and using interior backtracking line search technique each iterate switches to trial step of strict interior feasibility the nonmonotone criterion is used to speed up the convergence progress in the contours of objective function with large curvature theoretical analysis are given which prove that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions

global convergence of trust region interior point algorithms for infinite dimensional nonconvex minimization subject to pointwise bounds a class of interior point trust region algorithms for infinite dimensional nonlinear optimization subject to pointwise bounds in l p banach spaces 2 le p le infty is formulated and analyzed the problem formulation is motivated by optimal control problems with l p controls and pointwise control constraints the interior point trust region algorithms are generalizations of those recently introduced by coleman and li siam j optim 6 1996 pp 418 445 for finite dimensional problems many of the generalizations derived in this paper are also important in the finite dimensional context all first and second order global convergence results known for trust region methods in the finite dimensional setting are extended to the infinite dimensional framework of this paper