feasible and noninterior path following in constrained minimization with low multiplier regularity primal dual path following methods for constrained minimization problems in function space with low multiplier regularity are introduced and analyzed regularity properties of the path are proved the path structure allows us to define approximating models which are used for controlling the path parameter in an iterative process for computing a solution of the original problem the moreau yosida regularized subproblems of the new path following technique are solved efficiently by semismooth newton methods the overall algorithmic concept is provided and numerical tests including a comparison with primal dual path following interior point methods for state constrained optimal control problems show the efficiency of the new concept

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

the method of fundamental solutions for the numerical solution of the biharmonic equation abstract the method of fundamental solutions mfs is a relatively new technique for the numerical solution of certain elliptic boundary value problems it falls in the class of methods generally called boundary methods and like the well known boundary integral equation method is applicable when a fundamental solution of the differential equation is known in the mfs the approximate solution is a linear combination of fundamental solutions with singularities placed outside the domain of the problem the locations of the singularities are either preassigned or determined along with the coefficients of the fundamental solutions so that the approximate solution satisfies the boundary conditions as well as possible in many applications these quantities are determined by a least squares fit of the boundary conditions a nonlinear problem which is solved using standard software in this paper the mfs is formulated for biharmonic problems and is applied to a variety of standard test problems as well as to problems arising in elasticity and fluid flow

stabilized multiscale finite element method for the stationary navier stokes equations abstract in the paper a stabilized multiscale finite element method for the stationary incompressible navier stokes equations is considered the method is a petrov galerkin approach based on the multiscale enrichment of the standard polynomial space enriched with the unusual bubble functions which no longer vanish on every element boundary for the velocity space the stability of the p 1 p 0 triangular element or the q 1 p 0 quadrilateral element is established and the optimal error estimates of the stabilized multiscale finite element method for the stationary navier stokes equations are obtained

brief constrained linear state estimation a moving horizon approach this article considers moving horizon strategies for constrained linear state estimation additional information for estimating state variables from output measurements is often available in the form of inequality constraints on states noise and other variables formulating a linear state estimation problem with inequality constraints however prevents recursive solutions such as kalman filtering and consequently the estimation problem grows with time as more measurements become available to bound the problem size we explore moving horizon strategies for constrained linear state estimation in this work we discuss some practical and theoretical properties of moving horizon estimation we derive sufficient conditions for the stability of moving horizon state estimation with linear models subject to constraints on the estimate we also discuss smoothing strategies for moving horizon estimation our framework is solely deterministic

multi quadric quasi interpolation method coupled with fdm for the degasperis procesi equation in this paper the degasperis procesi dp equation which contains nonlinear high order derivatives and discontinuous solutions is recast to its equivalent form u p based on the equivalent formulation of dp equation a new numerical method is presented the multi quadric mq quasi interpolation method coupled with finite difference method is applied to approximate the spatial derivatives and the third order tvd method is used to approximate the time derivative several examples are presented to demonstrate the effectiveness of the proposed method

disturbance attenuation in finite spectrum assignment controllers two finite spectrum assignment controllers for continuous linear dynamic systems with multiple time delays in input signal are introduced the controllers are shown to comprise least squares state estimators disturbance attenuation properties stipulated by the choice of shift operator in the observers are studied

a semismooth newton cg method for constrained parameter identification in seismic tomography seismic tomography is a technique to determine the material properties of the earth s subsurface based on the observation of seismograms this can be stated as a pde constrained optimization problem governed by the elastic wave equation we present a semismooth newton pcg method with a trust region globalization for full waveform seismic inversion that uses a moreau yosida regularization to handle additional constraints on the material parameters we establish results on the differentiability of the parameter to state operator and analyze the proposed optimization method in a function space setting the elastic wave equation is discretized by a high order continuous galerkin method in space and an explicit newmark time stepping scheme the matrix free implementation relies on the adjoint based computation of the gradient and hessian vector products and on an mpi based parallelization numerical results are shown for an application in geophysical exploration at reservoir scale

generalized nash equilibrium problems in banach spaces theory nikaido isoda based path following methods and applications building upon the results in m hintermuller and t surowiec pac j optim 9 2013 pp 251 273 a class of noncooperative nash equilibrium problems is presented in which the feasible set of each player is perturbed by the decisions of their competitors via a convex constraint in addition for every vector of decisions a common state variable is given by the solution of an affine linear equation the resulting problem is therefore a generalized nash equilibrium problem gnep the existence of an equilibrium for this problem is demonstrated and first order optimality conditions are derived under a constraint qualification an approximation scheme is proposed which involves the solution of a parameter dependent sequence of standard nash equilibrium problems an associated path following strategy based on the nikaido isoda function is then proposed function space based numerics for parabolic gneps and a spot market model are developed

primal dual interior point methods for pde constrained optimization this paper provides a detailed analysis of a primal dual interior point method for pde constrained optimization considered are optimal control problems with control constraints in l p it is shown that the developed primal dual interior point method converges globally and locally superlinearly not only the easier l setting is analyzed but also a more involved l q analysis q is presented in l the set of feasible controls contains interior points and the frechet differentiability of the perturbed optimality system can be shown in the l q setting which is highly relevant for pde constrained optimization these nice properties are no longer available nevertheless a convergence analysis is developed using refined techniques in parti cular two norm techniques and a smoothing step are required the l q analysis with smoothing step yields global linear and local superlinear convergence whereas the l analysis without smoothing step yields only global linear convergence

a fast fourier galerkin method solving a boundary integral equation for the biharmonic equation we develop a fast fourier galerkin method for solving a boundary integral equation which is a reformulation of the dirichlet problem of the biharmonic equation the proposed method is based on a splitting of the resulting boundary integral operator that is we write the operator as a sum of two integral operators one having the fourier basis functions as eigenfunctions and the other whose representation matrix in the fourier basis can be compressed to a sparse matrix having only mathcal o n log n number of nonzero entries where n is the order of the fourier basis functions used in the method we then project the solution of the boundary integral equation onto the space spanned by the fourier basis functions this leads to a system of linear equations a fast solver for the system is based on a compression of its coefficient matrix we show that the method has the optimal convergence order mathcal o n q where q denotes the degree of regularity of the exact solution of the boundary int

a continuous time observer which converges in finite time it is shown that a continuous time observer which comprises two standard nth order observers and a delay d can observe the state of an nth order linear system in finite time d exactly in particular almost any convergence time d can be assigned independent of the observer eigenvalues

continuous least squares observers with applications a wide class of continuous least squares ls observers is treated in a common framework provided by the pseudodifferential operator paradigm it is shown that for the operators whose symbols satisfy certain conditions the continuous ls observer always exists providing observability of the plant the general result is illustrated by an ls observer stemming from a sliding window convolution operator applications to state feedback control and fault detection are discussed

source nodes on elliptic pseudo boundaries in the method of fundamental solutions for laplace s equation selection of pseudo boundaries abstract in the method of fundamental solutions mfs source nodes on circles outside the solution domains s has been widely applied in numerical computation in this paper source nodes on an ellipse are proposed for solving laplace s equation using the mfs and a robust error and stability analysis is established bounds on errors and condition numbers are derived for bounded simply connected domains polynomial convergence rates can be achieved but the exponential growth of the condition number is also obtained in previous stability analysis of the mfs circulant matrices have been always employed this is the first time the stability analysis is explored for non circular pseudo boundaries based on new techniques without using circulant matrices the criteria for evaluating numerical techniques are provided and some strategies for choosing pseudo boundaries are suggested

fir filters and recursive forms for continuous time invariant state space models an fir finite impulse response filter and an fir smoother are introduced for continuous time invariant state space models it is shown in this note that finite impulse responses of the fir filter and smoother can be easily determined by solving a simple riccati type matrix differential equation on a finite interval especially for systems with stationary processes finite impulse responses of the fir filter and smoother become time invariant and can be computed from simpler equations for fast computational purposes recursive forms of the fir filter and smoother are derived by using adjoint variables in this case all gains for recursive forms are shown to be constant

barrier methods for optimal control problems with convex nonlinear gradient state constraints in this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems governed by partial differential equations we will derive existence of solutions together with first order optimality conditions afterwards we show continuity of the central path together with convergence rates depending on the interior point parameter

state variable reconstruction abstract one of the problems in applying optimal control theory to practical optimal controller design is the need to know all the state variables a condition which is rarely satisfied no method is currently available for exactly reconstructing the state variables from the observable variables in this paper a method is developed for exact reconstruction of the state variables from the measurable variables

the multiplier penalty method for generalized nash equilibrium problems in banach spaces this paper deals with generalized nash equilibrium problems gneps in banach spaces we give an existence result for normalized equilibria of jointly convex gneps and then propose an augmented lag

path following methods for a class of constrained minimization problems in function space path following methods for primal dual active set strategies requiring a regularization parameter are introduced existence of a primal dual path and its differentiability properties are analyzed monotonicity and convexity of the primal dual path value function are investigated both feasible and infeasible approximations are considered numerical path following strategies are developed and their efficiency is demonstrated by means of examples

analysis of the method of fundamental solutions for the modified helmholtz equation the method of fundamental solutions mfs was first proposed by kupradze in 1963 since then the mfs has been extensively applied for solving various kinds of problems in science and engineering however few theoretical works have been reported in the literature in this paper we devote our work to the error analysis and stability of the mfs for the case of the modified helmholtz equation for disk domains a convergence analysis of the mfs was provided by li j comput appl math 159 113125 2004 for solving the modified helmholtz equation in this paper the error bounds of the mfs for bounded and simply connected domains are derived for smooth solutions of the modified helmholtz equation the exponential convergence rates can be achieved for analytic solutions the bounds of condition numbers of the mfs are derived for both disk domains and the bounded and simply connected domains to give the exponential growth via the number of fundamental solutions used numerical experiments are carried out to support the theoretical analysis moreover the analysis of this paper is applied to parabolic equations and some reviews of proof techniques and the analytical characteristics of the mfs are addressed

the trefftz method using fundamental solutions for biharmonic equations in this paper the trefftz method of fundamental solution fs called the method of fundamental solution mfs is used for biharmonic equations the bounds of errors are derived for the mfs with almansi s fundamental solutions denoted as the mafs in bounded simply connected domains the exponential and polynomial convergence rates are obtained from highly and finitely smooth solutions respectively the stability analysis of the mafs is also made for circular domains numerical experiments are carried out for both smooth and singularity problems the numerical results coincide with the theoretical analysis made when the particular solutions satisfying the biharmonic equation can be found the method of particular solutions mps is always superior to the mfs and the mafs based on numerical examples however if such singular particular solutions near the singular points do not exist the local refinement of collocation nodes and the greedy adaptive techniques can be used for seeking better source points based on the computed results the mfs using the greedy adaptive techniques may provide more accurate solutions for singularity problems moreover the numerical solutions by the mafs with almansi s fs are slightly better in accuracy and stability than those by the traditional mfs hence the mafs with the afs is recommended for biharmonic equations due to its simplicity

analysis on the method of fundamental solutions for biharmonic equations abstract in this paper the error and stability analysis of the method of fundamental solution mfs is explored for biharmonic equations the bounds of errors are derived for the fundamental solutions r 2 ln r in bounded simply connected domains and the polynomial convergence rates are obtained for certain smooth solutions the bounds of condition number are also derived to show the exponential growth rates for disk domains numerical experiments are carried out to support the above analysis which is the first time to provide the rigorous analysis of the mfs using r 2 ln r for biharmonic equations

on the equivalence of the trefftz method and method of fundamental solutions for laplace and biharmonic equations in this paper it is proved that the two approaches known in the literature as the method of fundamental solutions mfs and the trefftz method are mathematically equivalent in spite of their essentially minor and apparent differences in formulation in deriving the equivalence of the trefftz method and the mfs for the laplace and biharmonic problems it is interesting to find that the complete set in the trefftz method for the laplace and biharmonic problems are embedded in the degenerate kernels of the mfs the degenerate scale appears using the mfs when the geometrical matrix is singular the occurring mechanism of the degenerate scale in the mfs is also studied by using circulant the comparison of accuracy and efficiency of the two methods was addressed

the length of the primal dual path in moreau yosida based path following methods for state constrained optimal control a priori estimates of the length of the primal dual path resulting from a moreau yosida approximation of the feasible set for state constrained optimal control problems are derived these bounds d

brief a receding horizon unbiased fir filter for discrete time state space models this paper concerns with a new linear finite impulse response fir filter called the receding horizon unbiased fir rhuf filter for the state estimation in discrete time state space models to obtain the rhuf filter linearity unbiasedness and fir structure will be required beforehand in addition to a performance criteria of minimum variance the rhuf filter is obtained by directly solving an optimization problem with the unbiasedness constraint the rhuf filter has time invariance and deadbeat properties the rhuf filter is represented in both a batch form and an iterative form it is shown that the rhuf filter is equivalent to the existing receding horizon kalman fir rhkf filter whose optimality is not clear to understand the former is more systematic and logical while the latter is heuristic due to handling of infinite covariance of the initial state information

fundamental solutions method for elliptic boundary value problems we consider a procedure for solving boundary value problems for elliptic homogeneous equations known as the fundamental solutions method we prove its applicability for some second order operators as well as for fourth order ones the boundary conditions of an elliptic problem are approximated by using fundamental solutions of the corresponding operator with singularities located outside the domain of interest in a specific case of the laplacian an estimate shows that the method discussed possesses convergence properties as good as those of any method using harmonic polynomials as trial functions numerical examples are given among which are simple signorini s problems for harmonic and lame operators

change detection based on initial state estimation abstract a method of estimating initial states of single output linear time invariant dynamic system is presented by the use of the system models inputs and outputs fast detection of changes in dynamic systems is achieved using the estimated initial states

the method of fundamental solutions for annular shaped domains this paper consists of two parts in the first part we combine the analysis of bogomolny a bogomolny fundamental solutions method for elliptic boundary value problems siam journal on numerical analysis 22 1985 644 669 comodi and mathon m i comodi r mathon a boundary approximation method for fourth order problems mathematical models and methods in applied sciences 1 1991 437 445 and li et al z c li r mathon p sermer boundary methods for solving elliptic equations with singularities siam journal on numerical analysis 24 1987 487 498 for the method of fundamental solutions mfs and new error bounds are derived for the bounded simply connected in a readable approach a factor of o n is removed in the error bounds of bogomolny 1985 in the second part we extend the analysis for the annular domain s a by the mfs the other fundamental solutions are needed whose source nodes may also be located uniformly on a circle inside the domain s a as in the above reference error bounds are derived in detail to display the polynomial convergence rates

directional sensitivity of continuous least squares state estimators abstract least squares state estimators present an alternative to luenberger observers and yield an exact deadbeat estimate of the state vector of a dynamic system as the optimal solution to a least squares problem in some vector or functional space for instance the conventional l 2 optimal finite memory observer is shown to be a special case of the continuous least squares state estimator sensitivity of these estimators to structured uncertainty in the system matrix of the plant is studied using the frechet derivative it is shown that the state estimation error caused by the plant model s mismatch is proportional to the frechet derivative of the symbol of the parameterization operator used for the estimator implementation evaluated for the nominal value of the system matrix for the special case of state estimation in a single tone continuous oscillator the crucial impact of the parameterization operator choice on the state estimator sensitivity to the plant model s uncertainty is investigated in detail

the almansi method of fundamental solutions for solving biharmonic problems a new fundamental solutions method for the numerical solution of two dimensional biharmonic problems is described in this method which is based on the almansi representation of a biharmonic function in the plane the approximate solution is expressed in terms of fundamental solutions of laplace s equation and is determined by a least squares fit of the boundary conditions the results of numerical experiments which demonstrate the efficacy of the method are presented

formulation and numerical solution of nash equilibrium multiobjective elliptic control problems the formulation and the semismooth newton solution of nash equilibrium multiobjective elliptic optimal control problems are presented existence and uniqueness of a nash equilibrium are proved the corresponding solution is characterized by an optimality system that is approximated by second order finite differences and solved with a semismooth newton scheme it is demonstrated that the numerical solution is second order accurate and that the semismooth newton iteration is globally and locally quadratically convergent results of numerical experiments confirm the theoretical estimates and show the effectiveness of the proposed computational framework

a new preconditioner for indefinite and asymmetric matrices we present a novel preconditioner for numerical solutions of large sparse linear systems with indefinite and asymmetric matrices this new preconditioner named as product preconditioner ps is constructed by two fairly simple preconditioners the distribution of eigenvalues and the form of the eigenvectors of the preconditioned matrix are analyzed moreover an upper bound on the degree of the minimal polynomial is also studied numerical experiments with several examples show that the proposed ps performs better than block diagonal preconditioner bd and block triangular preconditioner bt as well as the constraint preconditioner sc in terms of the number of iteration and computational time

moreau yosida regularization in state constrained elliptic control problems error estimates and parameter adjustment an adjustment scheme for the regularization parameter of a moreau yosida based regularization or relaxation approach to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced the method utilizes error estimates of an associated finite element discretization of the regularized problems for the optimal selection of the regularization parameter in dependence on the mesh size of discretization and error estimates for the approximation error due to regularization the theoretical results are verified numerically