a reflective newton method for minimizing a quadratic function subject to bounds on some of the variables we propose a new algorithm a reflective newton method for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables this method applies to a general indefinite quadratic function for which a local minimizer subject to bounds is required and is particularly suitable for the large scale problem our new method exhibits strong convergence properties global and quadratic convergence and appears to have significant practical potential strictly feasible points are generated experimental results on moderately large and sparse problems support the claim of practicality for large scale problems

a quadratic programming approach to blind equalization and signal separation blind equalization and signal separation are two well established signal processing problems in this paper we present a quadratic programming algorithm for fast blind equalization and signal separation by introducing a special non mean square error mse objective function we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem based on a clear geometric interpretation and a formal proof we show that a perfect equalization solution is obtained at every local optimum of the quadratic program because blind source separation is by nature and mathematically a closely related problem we also generalize the algorithm for blind signal separation we show that by enforcing source orthogonalization through successive processing the quadratic programming approach can be applied effectively moreover the quadratic program is easily extendible to incorporate additional practical conditions such as jamming suppression constraints we also provide evidence of good performance through computer simulations

noncausal inverses for linear systems suppose we are to guide a plant with a square transfer matrix through a series of way points this can be accomplished by output tracking of trajectories which are fitted together in a sufficiently smooth manner each segment of each output is prescribed in terms of a polynomial or sine function or the product thereof our technique is to compute 1 a noncausal particular solution based on the desired trajectory over each segment and the movement from one segment to the next and this particular solution consists of a particular control and a particular state trajectory and 2 a regulator to handle modeling errors disturbances etc we concentrate on the particular solution

fulfilling hard constraints in uncertain linear systems by reference managing a method based on conceptual tools of predictive control is described for tackling tracking problems of uncertain linear systems wherein pointwise in time input and or state inequality constraints are present the method consists of adding to a primal compensated system a nonlinear device called predictive reference filter which manipulates the desired reference in order to fulfill the prescribed constraints provided that an admissibility condition on the initial state is satisfied the control scheme is proved to fulfill the constraints as well as stability and set point tracking requirements for all systems whose impulse step responses lie within given uncertainty ranges

symmetric tensor decomposition by an iterative eigendecomposition algorithm we present an iterative algorithm called the symmetric tensor eigen rank one iterative decomposition steroid for decomposing a symmetric tensor into a real linear combination of symmetric rank 1 unit norm outer factors using only eigendecompositions and least squares fitting originally designed for a symmetric tensor with an order being a power of two steroid is shown to be applicable to any order through an innovative tensor embedding technique numerical examples demonstrate the high efficiency and accuracy of the proposed scheme even for large scale problems furthermore we show how steroid readily solves a problem in nonlinear block structured system identification and nonlinear state space identification

a novel svm nda model for classification with an application to face recognition support vector machine svm is a powerful classification methodology where the support vectors fully describe the decision surface by incorporating local information on the other hand nonparametric discriminant analysis nda is an improvement over lda where the normality assumption is relaxed nda also detects the dominant normal directions to the decision plane this paper introduces a novel svm nda model which can be viewed as an extension to the svm by incorporating some partially global information especially discriminatory information in the normal direction to the decision boundary this can also be considered as an extension to the nda where the support vectors improve the choice of k nearest neighbors on the decision boundary by incorporating local information being an extension to both svm and nda it can deal with heteroscedastic and non normal data it also avoids the small sample size problem moreover it can be reduced to the classical svm model so that existing softwares can be used a kernel extension of the model called ksvm knda is also proposed to deal with nonlinear problems we have carried an extensive comparison of the svm nda to the lda svm heteroscedastic lda hlda nda and the combined svm and lda on artificial real and face recognition data sets results for ksvm knda have also been presented these comparisons demonstrate the advantages and superiority of our proposed model

towards a viscoelastic model for the unfused midpalatal suture development and validation using the midsagittal suture in new zealand white rabbits abstract maxillary expansion treatment is a commonly used procedure by orthodontists to widen a patient s upper jaw as this is typically performed in adolescent patients the midpalatal suture connective tissue adjoining the two maxilla halves remains unfused studies that have investigated patient response to expansion treatment generally through finite element analysis have considered this suture to behave in a linear elastic manner or it was left vacant the purpose of the study presented here was to develop a model that could represent the midpalatal suture s viscoelastic behavior quasilinear viscoelastic modified superposition schapery s and burgers modeling approaches were all considered raw data from a previously published study using new zealand white rabbits was utilized for model parameter estimation and validation in this study sentalloy coil springs at load levels of 0 49 n 50 g 0 98 n 100 g and 1 96 n 200 g were used to widen the midsagittal suture of live rabbits over a period of 6 weeks evaluation was based on a models ability to represent experimental data well over all three load sets ideally a single set of model constants could be used to represent data over all loads tested upon completion of the analysis it was found that the modified superposition method was able to replicate experimental data within one standard deviation of the means using a single set of constants for all loads future work should focus on model improvement as well as prediction of treatment outcomes

direct sampling method for identifying magnetic inhomogeneities in limited aperture inverse scattering problem abstract the direct sampling method dsm in limited aperture inverse scattering problems for transverse electric te polarization is considered based on the asymptotic expansion formula in the presence of small targets we demonstrate that the indicator function of dsm can be represented by an infinite series of bessel functions of integer order and correspondingly examine various properties of dsm simulation results with noisy data are created to support theoretical results based on the identified structure of the indicator function we design a new indicator function of dsm analyze its mathematical structure and generate simulation results to demonstrate its effectiveness and improvement

a smooth variational principle with applications to subdifferentiability and to differentiability of convex functions we show that typically lower semicontinuous functions on a banach space densely inherit lower subderivatives of the same degree of smoothness as the norm in particular every continuous convex function on a space with a g teaux weak hadamard frechet smooth renorm is densely g teaux weak hadamard frechet differentiable our technique relies on a more powerful analogue of ekeland s variational principle in which the function is perturbed by a quadratic like function this smooth variational principle has very broad applicability in problems of nonsmooth analysis

nonlinear inversion based output tracking an inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory in the case of minimum phase systems the trajectory produced agrees with that generated by hirschorn s inverse dynamic system however the preimage trajectory is noncausal rather than unstable in the nonminimum phase case in addition the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case with the addition of stabilizing feedback to the preimage trajectory asymptotically exact output tracking is achieved tracking is demonstrated with a numerical example and compared to the well known byrnes isidori regulator rather than solving a partial differential equation to construct a regulator the inverse is calculated using a picard like interaction when preactuation is not possible noncausal inverse trajectories can be truncated resulting in the tracking error transients found in other control schemes

convolution profiles for right inversion of multivariable non minimum phase discrete time systems the problem of the non causal inversion of linear multivariable discrete time systems is analyzed in the geometric approach framework and is solved through the computation of convolution profiles which guarantee perfect tracking under the assumption of infinite length preaction and postaction time intervals it is shown how the shape of the convolution profiles is related to both the relative degree and the invariant zeros of the plant a computational setting for the convolution profiles is derived by means of the standard geometric approach tools feasibility constraints are also taken into account a possible implementation scheme based on a finite impulse response system acting on a stabilized control loop is provided

optimal output transitions for linear systems this article addresses the optimal minimum input energy output transition problem for linear systems the goal is to transfer the output from an initial value y t email protected for all time t t f previous methods solve this output transition problem by transforming it into a state transition problem the initial and final states x t i x t f respectively are chosen and a minimum energy state to state transition problem is solved however the choice of the initial and final states can be ad hoc and the resulting output transition cost input energy may not be minimal the contribution of this article is the solution of the optimal output transition problem an example system with elastic dynamics is studied to illustrate the proposed method simulation results are presented that show substantial reduction of transition costs with the use of the proposed method when compared to the use of minimum energy state to state transitions

generalized foldy lax formulation we present a method for numerical wave propagation in a heterogeneous medium the medium is defined in terms of an extended scatterer or target which is surrounded by many small scatterers by extending the classic foldy lax formulation we developed an efficient algorithm for numerical wave propagation in two dimension in the method that we set forth multiple scattering among the point scatterers and the extended target is fully taken into account via a boundary integral formulation coupled with the foldy lax formulation this formulation forms the basis for our numerical procedure

brief optimal noncausal set point regulation of scalar systems this paper presents a novel system inversion approach to the set point regulation of linear scalar minimum phase systems this approach uses closed form expressions of cause effect pairs that make possible an arbitrarily smooth transition between two given output set points the cause effect pairs are based on the introduced concept of transition polynomials simple optimization procedures are then proposed to solve the relevant optimal output synthesis and optimal input synthesis the potentiality of the method is highlighted by the examples presented namely a synthesis of elevator velocity profiles and the performance improving of a pid controller

using stable input output inversion for minimum time feedforward constrained regulation of scalar systems the paper approaches the feedforward minimum time smooth control of non minimum phase linear scalar systems for set point regulation the aim is to synthesize a bounded input subject to non saturating constraints on the input and its derivatives till a prespecified arbitrary order the provided solution relies on a stable input output dynamic inversion technique and an ad hoc parameterized family of output transition functions the synthesized minimum time input that exhibits pre and post actuation is determined by means of easily implementable closed form expressions examples are given to illustrate the methodology

intrinsic dimension estimation via nearest constrained subspace classifier we consider the problems of classification and intrinsic dimension estimation on image data a new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation the distribution of the data in each class is modeled by a union of a finite number of affine subspaces of the feature space the affine subspaces have a common dimension which is assumed to be much less than the dimension of the feature space the subspaces are found using regression based on the 0 norm the proposed method is a generalisation of classical nn nearest neighbor nfl nearest feature line classifiers and has a close relationship to ns nearest subspace classifier the proposed classifier with an accurately estimated dimension parameter generally outperforms its competitors in terms of classification accuracy we also propose a fast version of the classifier using a neighborhood representation to reduce its computational complexity experiments on publicly available datasets corroborate these claims highlightsa new classifier called ncsc and its fast version called ncsc ii are proposed classifiers of nn nfl and ns are the special cases of ncsc ncsc ncsc ii can be used as intrinsic dimension estimator using well tuned intrinsic parameter ncsc ncsc ii outperforms nn nfl and ns

sparse representation in structured dictionaries with application to synthetic aperture radar sparse signal representations and approximations from overcomplete dictionaries have become an invaluable tool recently in this paper we develop a new heuristic graph structured sparse signal representation algorithm for overcomplete dictionaries that can be decomposed into subdictionaries and whose dictionary elements can be arranged in a hierarchy around this algorithm we construct a methodology for advanced image formation in wide angle synthetic aperture radar sar defining an approach for joint anisotropy characterization and image formation additionally we develop a coordinate descent method for jointly optimizing a parameterized dictionary and recovering a sparse representation using that dictionary the motivation is to characterize a phenomenon in wide angle sar that has not been given much attention before migratory scattering centers i e scatterers whose apparent spatial location depends on aspect angle finally we address the topic of recovering solutions that are sparse in more than one objective domain by introducing a suitable sparsifying cost function we encode geometric objectives into sar image formation through sparsity in two domains including the normal parameter space of the hough transform

formulation analysis and numerical study of an optimization based conservative interpolation remap of scalar fields for arbitrary lagrangian eulerian methods we develop and study the high order conservative and monotone optimization based remap obr of a scalar conserved quantity mass between two close meshes with the same connectivity the key idea is to phrase remap as a global inequality constrained optimization problem for mass fluxes between neighboring cells the objective is to minimize the discrepancy between these fluxes and the given high order target mass fluxes subject to constraints that enforce physically motivated bounds on the associated primitive variable density in so doing we separate accuracy considerations handled by the objective functional from the enforcement of physical bounds handled by the constraints the resulting obr formulation is applicable to general unstructured heterogeneous grids under some weak requirements on grid proximity but not on the cell types we prove that the obr algorithm is linearity preserving in one two and three dimensions the paper also examines connections between the obr and the recently proposed flux corrected remap fcr liska et al 1 we show that the fcr solution coincides with the solution of a modified version of obr m obr which has the same objective but a simpler set of box constraints derived by using a worst case scenario because m obr fcr has a smaller feasible set preservation of linearity may be lost and accuracy may suffer for some grid configurations our numerical studies confirm this and show that obr delivers significant increases in robustness and accuracy preliminary efficiency studies of obr reveal that it is only a factor of 2 1 slower than fcr but admits 1 5 times larger time steps

the drop theorem the petal theorem and ekeland s variational principle on montre que le principe variationnel d ekeland ou plus precisement une forme legerement modifiee est une consequence d un resultat geometrique connu sous le terme de theoreme de la goutte

adjoint method for a tumor invasion pde constrained optimization problem in 2d using adaptive finite element method in this paper we present a method for estimating an unknown parameter that appears in a two dimensional non linear reaction diffusion model of cancer invasion this model considers that tumor induced alteration of micro environmental ph provides a mechanism for cancer invasion a coupled system reaction diffusion describing this model is given by three partial differential equations for the 2d non dimensional spatial distribution and temporal evolution of the density of normal tissue the neoplastic tissue growth and the excess h ion concentration each of the model parameters has a corresponding biological interpretation for instance the growth rate of neoplastic tissue the diffusion coefficient the re absorption rate and the destructive influence of h ions in the healthy tissue the parameter is estimated by solving a minimization problem in which the objective function is defined in order to compare both the real data and the numerical solution of the cancer invasion model the real data can be obtained by for example fluorescence ratio imaging microscopy we apply a splitting strategy joint with the adaptive finite element method to numerically solve the model the minimization problem the inverse problem is solved by using a gradient based optimization method in which the functional derivative is provided through an adjoint approach

a b spline based pseudo inversion approach for constrained optimal output transition the contribution of this paper is to propose a new method for the continuous time optimal output transition problem under constraints on the control effort the new method situates in the recently

the explicit linear quadratic regulator for constrained systems we present a technique to compute the explicit state feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints we show that this closed form solution is piecewise linear and continuous as a practical consequence of the result constrained linear quadratic regulation becomes attractive also for systems with high sampling rates as on line quadratic programming solvers are no more required for the implementation

an efficient algorithm for the generalized foldy lax formulation consider the scattering of a time harmonic plane wave incident on a two scale heterogeneous medium which consists of scatterers that are much smaller than the wavelength and extended scatterers that are comparable to the wavelength in this work we treat those small scatterers as isotropic point scatterers and use a generalized foldy lax formulation to model wave propagation and capture multiple scattering among point scatterers and extended scatterers our formulation is given as a coupled system which combines the original foldy lax formulation for the point scatterers and the regular boundary integral equation for the extended obstacle scatterers the existence and uniqueness of the solution for the formulation is established in terms of physical parameters such as the scattering coefficient and the separation distances computationally an efficient physically motivated gauss seidel iterative method is proposed to solve the coupled system where only a linear system of algebraic equations for point scatterers or a boundary integral equation for a single extended obstacle scatterer is required to solve at each step of iteration the convergence of the iterative method is also characterized in terms of physical parameters numerical tests for the far field patterns of scattered fields arising from uniformly or randomly distributed point scatterers and single or multiple extended obstacle scatterers are presented

nonnegative least correlated component analysis for separation of dependent sources by volume maximization although significant efforts have been made in developing nonnegative blind source separation techniques accurate separation of positive yet dependent sources remains a challenging task in this paper a joint correlation function of multiple signals is proposed to reveal and confirm that the observations after nonnegative mixing would have higher joint correlation than the original unknown sources accordingly a new nonnegative least correlated component analysis nlca method is proposed to design the unmixing matrix by minimizing the joint correlation function among the estimated nonnegative sources in addition to a closed form solution for unmixing two mixtures of two sources the general algorithm of nlca for the multisource case is developed based on an iterative volume maximization ivm principle and linear programming the source identifiability and required conditions are discussed and proven the proposed nlca algorithm denoted by nlca ivm is evaluated with both simulation data and real biomedical data to demonstrate its superior performance over several existing benchmark methods

barrier function based model predictive control a new formulation of nonlinear model predictive control mpc is developed by including a weighted barrier function in the control objective while the barrier ensures that inequality constraints are strictly satisfied it also provides a smooth transition between points in the interior and those on the boundary of the constraint set in addition the resulting optimisation problem to be solved at each control step is effectively unconstrained and thus amenable to elegant optimisation techniques the barrier must satisfy certain conditions in order that the state converges to the origin and we show how to construct such a barrier conventional mpc may be seen as a limiting case of the new class as the barrier weighting itself approaches zero we pay particular attention to the novel approach of fixing the weighting parameter to some positive value possibly large and observe that this provides a degree of controller caution near constraint boundaries we construct an ellipsoidal invariant set by exploiting the geometry of self concordant functions and show nominal closed loop stability for this class of controllers under full state feedback

a preconditioning framework for sequences of diagonally modified linear systems arising in optimization we propose a framework for building preconditioners for sequences of linear systems of the form a delta k x k b k where a is symmetric positive semidefinite and delta k is diagonal positive semidefinite such sequences arise in several optimization methods e g in affine scaling methods for bound constrained convex quadratic programming and bound constrained linear least squares as well as in trust region and overestimation methods for convex unconstrained optimization problems and nonlinear least squares for all the matrices of a sequence the preconditioners are obtained by updating any preconditioner for a available in the ldl t form the preconditioners in the framework satisfy the natural requirement of being effective on slowly varying sequences furthermore under an additional property they are also able to cluster eigenvalues of the preconditioned matrix when some entries of delta k are sufficiently large we present two low cost preconditioners sharing the above mentioned p

a p version finite element method for nonlinear elliptic variational inequalities in 2d this article introduces and analyzes a p version fem for variational inequalities resulting from obstacle problems for some quasi linear elliptic partial differential operators we approximate the solution by controlling the obstacle condition in images of the gauss lobatto points we show existence and uniqueness for the discrete solution up from the p version for the obstacle problem we prove the convergence of up towards the solution with respect to the energy norm and assuming some additional regularity for the solution we derive an a priori error estimate in numerical experiments the p version turns out to be superior to the h version concerning the convergence rate and the number of unknowns needed to achieve a certain exactness of the approximation

nonnegative blind source separation by sparse component analysis based on determinant measure the problem of nonnegative blind source separation nbss is addressed in this paper where both the sources and the mixing matrix are nonnegative because many real world signals are sparse we deal with nbss by sparse component analysis first a determinant based sparseness measure named d measure is introduced to gauge the temporal and spatial sparseness of signals based on this measure a new nbss model is derived and an iterative sparseness maximization ism approach is proposed to solve this model in the ism approach the nbss problem can be cast into row to row optimizations with respect to the unmixing matrix and then the quadratic programming qp technique is used to optimize each row furthermore we analyze the source identifiability and the computational complexity of the proposed ism qp method the new method requires relatively weak conditions on the sources and the mixing matrix has high computational efficiency and is easy to implement simulation results demonstrate the effectiveness of our method

the strong ekeland variational principle the strong drop theorem and applications on donne une nouvelle demonstration du theoreme de la goutte generalisee en utilisant des formes renforcees du principe variationnel d ekeland et du theoreme de la goutte et donne de nouveaux resultats et de nouvelles demonstrations de resultats connus sur les proprietes generiques des problemes de minimisation convexes et non convexes