optimal control for nonconvex rate independent evolution processes energetic solutions to rate independent systems allow for an effective modeling of many physical systems displaying hysteretic effects e g phase transformations in shape memory alloys elastoplasticity and ferroelectricity for some engineering applications optimal control of such systems is desirable we establish existence results for these continuous time optimal control problems by a combination of the direct method with gamma convergence arguments applicability to the common situation of a controlled external loading is demonstrated and a concrete partial differential inclusion as well as an academic model of the foreign exchange market including trading costs are investigated

minimax control of nonlinear evolution equations in this paper we study nonlinear parametric optimal control problems we formulate the relevant minimax problem and prove the existence of an optimal control also we derive necessary conditions for saddle point optimality we also associate to the original optimization problem a dual problem and then for the pair we prove a complete duality theorem finally we present two examples of parabolic distributed parameter systems which illustrate the abstract results

minimax control of nonlinear evolution equations in this paper we study nonlinear parametric optimal control problems we formulate the relevant minimax problem and prove the existence of an optimal control also we derive necessary conditions for saddle point optimality we also associate to the original optimization problem a dual problem and then for the pair we prove a complete duality theorem finally we present two examples of parabolic distributed parameter systems which illustrate the abstract results

relaxation in nonconvex optimal control problems described by fractional differential equations abstract we consider the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a control system described by fractional differential equation with mixed nonconvex constraints on the control a relaxation problem is treated along with the original problem it is proved that under general assumptions the relaxation problem has an optimal solution and that for each optimal solution there is a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory the control and the functional in appropriate topologies simultaneously

continuity in the parameter of the minimum value of an integral functional over the solutions of an evolution control system abstract the problem of minimization of an integral functional with an integrand that is nonconvex with respect to the control is considered we minimize our functional over the solution set of a nonlinear evolution control system with a time dependent subdifferential operator in a hilbert space the control constraint is given by a nonconvex closed bounded set the integrand the control constraint the initial conditions and the operators in the equation describing the control system all depend on a parameter we consider along with the original problem the problem of minimizing an integral functional with an integrand convexified with respect to the control over the solution set of the same system but now subject to the convexified control constraint by a solution of the control system we mean a trajectory control pair we prove that for each value of the parameter the convexified problem has a solution which is the limit of a minimizing sequence of the original problem and the minimum value of the functional of the convexified problem is a continuous function of the parameter these abstract results are used to study a quasilinear parabolic system

the computation of the principal square roots of centrosymmetric h matrices in this paper two algorithms for computing the principal square root of a centrosymmetric h matrix with positive diagonal entries are proposed it is showed that our algorithms ensure significant savings in computational costs as compared to the case of an arbitrary h matrix a with positive diagonal entries

computationally efficient maximum likelihood estimation of structured covariance matrices by invoking the extended invariance principle exip we present herein a computationally efficient method that provides asymptotic for large samples maximum likelihood aml estimation for structured covariance matrices and is referred to as the aml algorithm a closed form formula for estimating the hermitian toeplitz covariance matrices that makes aml computationally simpler than most existing hermitian toeplitz matrix estimation algorithms is derived although the aml covariance matrix estimator can be used in a variety of applications we focus on array processing our simulation study shows that aml enhances the performance of angle estimation algorithms such as music by making them very close to the corresponding cramer rao bound crb for uncorrelated signals numerical comparisons with several structured and unstructured covariance matrix estimators are also presented

doubly nonlinear evolution equations governed by time dependent subdifferentials in reflexive banach spaces abstract we prove the existence of solutions of the cauchy problem for the doubly nonlinear evolution equation d v t d t v t u t f t v t h u t 0 t t where h respectively v t denotes the subdifferential operator of a proper lower semicontinuous functional respectively t explicitly depending on t from a hilbert space h respectively reflexive banach space v into and f is given to do so we suppose that v h h v compactly and densely and we also assume smoothness in t boundedness and coercivity of t in an appropriate sense but use neither strong monotonicity nor boundedness of h the method of our proof relies on approximation problems in h and a couple of energy inequalities we also treat the initial boundary value problem of a non autonomous degenerate elliptic parabolic problem

signal enhancement a composite property mapping algorithm a signal enhancement algorithm is developed that seeks to recover a signal from noise contaminated distorted measurements made on that signal this object is achieved by utilizing a set of properties which the signal is known or is hypothesized as possessing the measured signal is modified to the smallest degree necessary to sequentially possess each of the individual properties conditions for the algorithm s convergence are established in which the primary requirement is that a composite property mapping be closed this is a relatively unrestricted condition in comparison to that required of most existing signal enhancement algorithms

optimal control of multivalued quasi variational inequalities abstract optimal control of various variational problems has been an area of active research on the other hand in recent years many important models in mechanics and economics have been formulated as multi valued quasi variational inequalities the primary objective of this work is to study optimal control of the general nonlinear problems of this type under suitable conditions we ensure the existence of an optimal control for a quasi variational inequality with multivalued pseudo monotone maps convergence behavior of the control is studied when the data for the state quasi variational inequality is contaminated by some noise some possible applications are discussed

boundary hemivariational inequality of parabolic type abstract in this paper we consider a parabolic hemivariational inequality with a nonmonotone multivalued boundary condition and with a time dependent pseudomonotone operator we establish the existence of solutions for such inequality our proof is based on a known surjectivity result for operators of pseudomonotone type we present an example of semipermeability heat conduction problem to which the result applies

the optimal control of a new class of impulsive stochastic neutral evolution integro differential equations with infinite delay abstractin this paper we introduce the optimal control problems governed by a new class of impulsive stochastic partial neutral evolution equations with infinite delay in hilbert spaces first by using stochastic analysis the analytic semigroup theory fractional powers of closed operators and suitable fixed point theorems we prove an existence result of mild solutions for the control systems in the norm without the assumptions of compactness next we derive the existence conditions of optimal pairs of these systems finally application to a nonlinear impulsive stochastic parabolic optimal control system is considered

degenerate asymptotic perturbation theory asymptotic rayleigh schrodinger perturbation theory for discrete eigenvalues is developed systematically in the general degenerate case for this purpose we study the spectral properties ofm m matrix functionsa of a complex variable which have an asymptotic expansion ea k k as 0 we show that asymptotic expansions for groups of eigenvalues and for the corresponding spectral projections ofa can be obtained from the set a by analytic perturbation theory special attention is given to the case wherea is borel summable in some sector originating from 0 with opening angle here we prove that the asymptotic series describe individual eigenvalues and eigenprojections ofa which are shown to be holomorphic ins near 0 and borel summable ifa k a k for allk we then fit these results into the scheme of rayleigh schrodinger perturbation theory and we give some examples of asymptotic estimates for schrodinger operators

existence results for quasilinear parabolic hemivariational inequalities abstract this paper is devoted to the periodic problem for quasilinear parabolic hemivariational inequalities at resonance as well as at nonresonance by use of the theory of multi valued pseudomonotone operators the notion of generalized gradient of clarke and the property of the first eigenfunction we build a landesman lazer theory in the nonsmooth framework of quasilinear parabolic hemivariational inequalities

optimal control for doubly nonlinear evolutionary inclusions abstract we study the optimal control of systems for a class of nonlinear hemivariational inequalities which are in the form of evolutionary inclusions involving clarke s generalized gradient the control variables are introduced both in the generalized gradient and in the source terms we first establish the existence of weak solutions to nonlinear inclusions and prove the upper semicontinuity property of their solution sets then we present the minimization problem and show the existence of optimal admissible state control pairs finally some examples of our abstract results which appear in applications are discussed

bogolyubov type theorem with constraints induced by a control system with hysteresis effect abstract we consider the problem of minimization of an integral functional with nonconvex with respect to the control integrand we minimize our functional over the solution set of a control system described by two ordinary differential equations subject to a control constraint given by a multivalued mapping with closed nonconvex values the coefficients of the equations and the constraint depend on the phase variables one of the equations contains the subdifferential of the indicator function of a closed convex set depending on the unknown phase variable the equation containing the subdifferential describes an input output relation of hysteresis type along with the original problem we also consider the problem of minimizing the integral functional with the convexified with respect to the control integrand over the solution set of the same system with the convexified control constraint under sufficiently general assumptions we prove that this relaxed problem has an optimal solution which is the limit of a minimizing sequence of the original problem the convergence takes place simultaneously with respect to the trajectory the control and the functional and is uniform in appropriate topologies

optimal control for a class of strongly nonlinear impulsive equations in banach spaces abstract in this paper we consider the optimal control problem of system governed by a class of strongly nonlinear impulsive evolution equations based on the existence of strongly nonlinear impulsive evolution equations which contain nonlinear monotone operators and nonmonotone perturbations we prove the existence of optimal controls for the general lagrange problem the necessary conditions for optimality are also presented

computing the square roots of matrices with central symmetry for computing square roots of a nonsingular matrix a which are functions of a two well known fast and stable algorithms which are based on the schur decomposition of a were proposed by bjork and hammarling a bjork s hammarling a schur method for the square root of a matrix linear alg appl 52 53 1983 127 140 for square roots of general complex matrices and by higham n j higham computing real square roots of a real matrix linear alg appl 88 89 1987 405 430 for real square roots of real matrices in this paper we further consider the computation of the square roots of matrices with central symmetry we first investigate the structure of the square roots of these matrices and then develop several algorithms for computing the square roots we show that our algorithms ensure significant savings in computational costs as compared to the use of standard algorithms for arbitrary matrices

strongly nonlinear impulsive evolution equations and optimal control abstract strongly nonlinear impulsive evolution equations are investigated existence of solutions of strongly nonlinear impulsive equations is proved and some properties of the solutions are discussed these results are applied to lagrange problems of optimal control and we proved existence results for illustration an example of a quasi linear impulsive parabolic differential equation and the corresponding optimal control is also presented

boundary hemivariational inequality problems with doubly nonlinear operators in this paper we investigate a class of nonlinear boundary hemivariational inequality problems under suitable hypotheses the existence of solutions is established via rewriting these problems into a class of evolution inclusions and using the discretization method and the theory of pseudomonotone operators moreover the continuous dependence result of the solutions to the initial data is given

spectral analysis and stability properties of a relativistic deformation of the harmonic oscillator the spectral properties are established and the stability of the eigenvalues under the singular perturbation representing the relativistic corrections are proven for a family of ordinary differential operators describing a relativistic deformation of the quantum harmonic oscillator

existence and regularity results for doubly nonlinear inclusions with nonmonotone perturbation abstract this paper deals with a class of nonlinear evolution inclusions arising from enthalpy formulation of heat conduction problems with phase change and nonmonotone source using time discretization technique and monotone operators theory we show the existence of weak solutions then we prove strong convergence of approximate solutions and lift regularity of the weak solutions under appropriate conditions moreover application to physical model described by hemivariational inequality is given

the computation of the square roots of circulant matrices abstract in the first part of this paper we investigate the reduced forms of circulant matrices and quasi skew circulant matrices by using their properties we present two efficient algorithms to compute the square roots of circulant matrices and quasi skew circulant matrices respectively those methods are faster than the traditional algorithm which is based on the schur decomposition in the second part we further consider circulant h matrices with positive diagonal entries and develop two algorithms for computing their principal square roots those two algorithms have the common advantage that is they only need matrix matrix multiplications in their iterative sequences an operation which can be done very efficiently on modern high performance computers

some properties of centrosymmetric matrices in this paper some properties of centrosymmetric matrices which often appear in the construction of orthonormal wavelet basis in wavelet analysis are investigated

degenerate type fractional evolution hemivariational inequalities and optimal controls via fractional resolvent operators in this paper we mainly investigate controlled fractional evolution hemivariational inequalities of degenerate type in caputo and riemann liouville fractional derivatives of order in 1 2 respect

the brezis ekeland principle for doubly nonlinear equations the celebrated brezis ekeland principle c r acad sci paris ser a b 282 1976 pp ai a1197 a1198 aii and a971 a974 characterizes trajectories of nonautonomous gradient flows of convex functionals as solutions to suitable minimization problems this note extends this characterization to doubly nonlinear evolution equations driven by convex potentials the characterization is exploited in order to establish approximation results for gradient flows doubly nonlinear equations and rate independent evolutions

exponentially accurate error estimates of quasiclassical eigenvalues ii several dimensions we study the behavior of truncated rayleigh schrodinger series for low lying eigenvalues of the time independent schrodinger equation in the semiclassical limit 0 in particular we prove that if the potential energy satisfies certain conditions there is an optimal truncation of the series for the eigenvalues in the sense that this truncation is exponentially close to the exact eigenvalue these results were already discussed for the one dimensional case in a previous article this time we consider the multi dimensional problem where degeneracy plays a central role

on seminormality of integral functionals and their integrands we present a definition of seminormality which extends classical notions due to tonelli fondamenti di calcolo delle variazioni 1921 mcshane ann scuola norm sup pisa 2 3 1934 pp 181 211 287 315 and cesari traps amer math soc 124 1966 pp 369 412 j optim theory appl 6 1970 pp 114 137 siam j control optim 9 1971 pp 287 315 and applies to both integrands seminormality in the small and their integral functionals seminormality in the large our main result states that under very general hypotheses seminormality in the small and large are equivalent by introducing a notion called nagumo tightness we show that the usual sufficient conditions for the lower semicontinuity of an integral functional also imply a form of seminormality of the integral functional necessary conditions for the lower semicontinuity of an integral functional can also be obtained from our results

computing real square roots of a real matrix bjorck and hammarling 1 describe a fast stable schur method for computing a square root x of a matrix a x2 a we present an extension of their method which enables real arithmetic to be used throughout when computing a real square root of a real matrix for a nonsingular real matrix a conditions are given for the existence of a real square root and for the existence of a real square root which is a polynomial in a the number of square roots of the latter type is determined the conditioning of matrix square roots is investigated and an algorithm is given for the computation of a well conditioned square root

a schur method for the square root of a matrix abstract a fast and stable method for computing the square root x of a given matrix a x 2 a is developed the method is based on the schur factorization a qsq h and uses a fast recursion to compute the upper triangular square root of s it is shown that if x 2 a is not large then the computed square root is the exact square root of a matrix close to a the method is extended for computing the cube root of a matrices exist for which the square root computed by the schur method is ill conditioned but which nonetheless have well conditioned square roots an optimization approach is suggested for computing the well conditioned square roots in these cases

quantum degeneracy and classical perturbation theory the degenerate rayleigh schrodinger perturbation theory for the eigenvalues of the class of schrodinger operators s e s0 ev where s0 is the laplace beltrami operator on the one dimensional torus t1 and v is an analytic potential perturbed rotator is explicitly constructed by means of the algorithm of the classical resonant birkhoff normal form as a consequence the degenerate quantum perturbation theory tends to the classical one in the classical limit

cyclic thermodynamic processes and entropy production we study the time evolution of a periodically driven quantum mechanical system coupled to several reservoirs of free fermions at different temperatures this is a paradigm of a cyclic thermodynamic process we introduce the notion of a floquet liouvillean as the generator of the dynamics of the coupled system on an extended hilbert space we show that the time periodic state which the state of the coupled system converges to after very many periods corresponds to a zero energy resonance of the floquet liouvillean we then show that the entropy production per cycle is strictly positive a property that implies carnot s formulation of the second law of thermodynamics

on parametric evolution inclusions of the subdifferential type with applications to optimal control problems in this paper we study parametric evolution inclusions of the subdifferential type and their applications to the sensitivity analysis of nonlinear infinite dimensional optimal control problems the parameter appears in all the data of the problem including the subdifferential operator first we establish several continuity results for the solution multifunction of the subdifferential inclusion then we study how these results can be used to examine the sensitivity properties variational stability of certain broad classes of nonlinear infinite dimensional optimal control problems some examples are worked out in detail illustrating the applicability of our work these include obstacle problems with time varying obstacles optimal control of distributed parameter systems and differential variational inequalities

evolution hemivariational inequality for a class of dynamic viscoelastic nonmonotone frictional contact problems in this paper we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation the friction condition is described by a multivalued subdifferential relation which includes both the slip displacement and the slip rate dependent friction and the tresca models the existence of weak solutions to the problem is proved by exploiting a surjectivity result for a class of pseudomonotone mappings

temporal exponential decay for the stark effect in atoms abstract let h 1 i 1 n i v x i 1 i x i x j 1 v x i n x y 1 y d y with a normalized gaussian suppose e 0 and that h h 1 e i 1 n x i has no eigenfunctions in l 2 r 3n if h 1 with ess h 1 then e ith decays exponentially at a rate governed by the positions of the resonances of h

on the convergence of solutions of multivalued parabolic equations and applications abstract in this paper we examine parametric nonlinear parabolic problems with multivalued terms using a general notion of g convergence for such operators we prove a convergence theorem for the solution sets of the corresponding cauchy dirichlet problem we also study a related minimax control problem

on asymptotic perturbation theory for quantum mechanics almost invariant subspaces and gauge invariant magnetic perturbation theory singular perturbation theory for quantum mechanics is considered in a framework generalizing the spectral concentration theory under very general conditions asymptotic estimations on the rayleigh schrodinger expansions of the perturbed spectral projections are obtained as a consequence almost invariant subspaces of exponential order are constructed the results cover practically all singular perturbations considered in nonrelativistic quantum mechanics in the magnetic field case under the condition that the magnetic field does not increase at infinity a gauge invariant perturbation theory leading to convergent series with field dependent coefficients is developed

canonical expansion of symmetric operators and perturbation theory let h be any symmetric schrodinger operator of the type 2 x21 x2d igw x1 xd on where w is any odd homogeneous polynomial and it is proved that is self adjoint and that its eigenvalues coincide up to a sign with the singular values of h i e the eigenvalues of moreover we explicitly construct the canonical expansion of h and determine the singular values j of h through the borel summability of their divergent perturbation theory the singular values yield estimates of the location of the eigenvalues j of h by weyl s inequalities

a class of nonlinear elliptic parabolic equations with time dependent constraints on etudie les equations d evolutions non lineaires de la forme f t du t dt t v t v t bu t 0 t t dans un espace de hilbert h ou t est la sous differentielle d une fonction convexe t definie sur h b est un operateur monotone maximal dans h on considere l existence et l unicite des solutions ainsi que des estimations a priori

computing matrix vector products with centrosymmetric and centrohermitian matrices an algorithm proposed recently by melman reduces the costs of computing the product ax with a symmetric centrosymmetric matrix a as compared to the case of an arbitrary a we show that the same result can be achieved by a simpler algorithm which requires only that a be centrosymmetric however if a is hermitian or symmetric this can be exploited to some extent also we show that similar gains are possible when a is a skew centrosymmetric or a centrohermitian matrix

a dynamic frictional contact problem for piezoelectric materials we consider a mathematical model which describes the frictional contact between a piezoelectric body and an electrically conductive foundation the process is dynamic the material s behavior is modeled with an electro viscoelastic constitutive law and the contact is described by subdifferential boundary conditions we derive the variational formulation of the problem which is in the form of a system involving a second order evolutionary hemivariational inequality for the displacement field coupled with a time dependent hemivariational inequality for the electric potential field then we prove the existence of a unique weak solution to the model the proof is based on arguments of abstract second order evolutionary inclusions with monotone operators

existence and convergence theorems for doubly nonlinear partial differential equations of elliptic parabolic type here t 0 v u ax au ax au ax and b is a map from rn x 0 t x r x rn into r for each i 1 n satisfying certain conditions to be specified at a later time a precise formulation of 1 1 is given in section 3 for given u0 and f we study the existence of weak solutions of 1 1 although doubly nonlinear equations of the type 1 1 are of mathematical interest in their own right they arise as a model for a variety of diffusion problems in particular they comprise in a unifying scheme free boundary problems of different natures an example situation is nonstationary saturated unsaturated flow of an incompressible fluid through a porous medium in the case of time dependent water levels a weak formulation of this problem leads to equations of the type 1 1 see 2 however a large held of application for our results is the diffusion problem involving a solid liquid phase change of the stefan type an architypical example is heat transfer during solidification in a nonhomogeneous 205

extremal solutions of quasilinear parabolic inclusions with generalized clarke s gradient abstract in this paper we consider an initial boundary value problem for a parabolic inclusion whose multivalued nonlinearity is characterized by clarke s generalized gradient of some locally lipschitz function and whose elliptic operator may be a general quasilinear operator of leray lions type recently extremality results have been obtained in case that the governing multivalued term is of special structure such as multifunctions given by the usual subdifferential of convex functions or subgradients of so called dc functions the main goal of this paper is to prove the existence of extremal solutions within a sector of appropriately defined upper and lower solutions for quasilinear parabolic inclusions with general clarke s gradient the main tools used in the proof are abstract results on nonlinear evolution equations regularization comparison truncation and special test function techniques as well as tools from nonsmooth analysis

on the optimal control of strongly nonlinear evolution equations abstract in this paper we study optimal control problems governed by nonlinear evolution equations with nonmonotone nonlinearities in the state first we prove an existence theorem then using the penalty method we obtain necessary conditions for optimality from them we derive a bang bang characterization of optimal controls finally an example of a nonlinear parabolic optimal control system is worked out in detail

necessary and sufficient conditions for l 1 strong weak lower semicontinuity of integral functionals soit t 7b f un espace fini de mesure nonatomique x ii ii un espace de banach non separable et v i i un espace de banach reflexif separable dont v est le dual soit f txxxv une fonction 7b f 7b b x v mesurable on etudie l integrale fonctionnelle associee i f l x 1 l v 1 definie par if x v f r x t v t dt

a pseudo monotonicity adapted to doubly nonlinear elliptic parabolic equations the case where b is an unbounded linear operator was considered 1rst by bardos and br7 ezis 4 in the nonlinear case raviart 20 grange and mignot 13 dibenedetto and showalter 11 proved existence results assuming that a and b are at least monotone operators and b is compact alt and luckhaus 1 investigated the case of a non compact operator b assuming a is strongly monotone their work was extended more recently by ka cur 14 filo and ka cur 12 or zadrzy7 nska and zajb aczkowski 26 berm7 udez et al 7 devoted their work to the case where b is compact and strongly monotone and a is pseudo monotone we are interested in the same case excepted that b is no longer assumed to be strongly monotone thus the equation may

an existence theorem for evolution inclusions involving opposite monotonicities in this paper we examine evolution inclusions of the subdifferential type with the set valued perturbation being nonconvex valued and dissipative under certain generally mild hypotheses on the data we prove the existence of a strong global solution extending earlier analogous results by m otani and a cellina v staicu an example of a distributed parameter system is also presented in detail

exponentially accurate error estimates of quasiclassical eigenvalues we study the behaviour of truncated rayleigh schrodinger series for the low lying eigenvalues of the one dimensional time independent schrodinger equation in the semiclassical limit 0 under certain hypotheses on the potential v x we prove that for any given small 0 there is an optimal truncation of the series for the approximate eigenvalues such that the difference between an approximate and exact eigenvalue is smaller than exp c for some positive constant c we also prove the analogous results concerning the eigenfunctions

relaxation and optimisation of a phase field control system with hysteresis abstractthe present paper is concerned with a nonlinear partial differential control system arising in phase transition modelling the control constraint is given by a state dependent nonconvex valued multivalued mapping we study the problem of minimisation of a given integral cost functional over solutions to the above system the cost integrand is nonconvex in the control variable relaxation results of bogolyubov type are obtained for this problem

stability of schrodinger eigenvalue problems we derive a general stability criterion for discrete eigenvalues of schrodinger operators such asa p 2 v x using only strong continuity ofa anda in the perturbation parameter the theory is developed for non selfadjoint operators and illustrated with examples like the anharmonic oscillator the stark and the zeeman effect the principal tools are weyl s criterion for the essential spectrum and a construction due to enss 5 they are also used to extend the classical invariance theorems for the essential spectrum to certain singular perturbations including some local perturbations of the laplacian by differential operators of arbitrary high order