the complex parameter rao test the rao test is an important method in signal detection in the presence of unknown parameters the traditional approach to the problem when the unknown parameters are complex valued is to form a corresponding real valued parameter vector and then to use the real rao test alternatively we present a complex parameter rao test by reformulating the calculations with respect to the complex valued quantities directly two important examples of the application of the complex parameter rao test are given to illustrate the procedure

some projection methods with the bb step sizes for variational inequalities since the appearance of the barzilai borwein bb step sizes strategy for unconstrained optimization problems it received more and more attention of the researchers it was applied in various fields of the nonlinear optimization problems and recently was also extended to optimization problems with bound constraints in this paper we further extend the bb step sizes to more general variational inequality vi problems i e we adopt them in projection methods under the condition that the underlying mapping of the vi problem is strongly monotone and lipschitz continuous and the modulus of strong monotonicity and the lipschitz constant satisfy some further conditions we establish the global convergence of the projection methods with bb step sizes a series of numerical examples are presented which demonstrate that the proposed methods are convergent under mild conditions and are more efficient than some classical projection like methods

on the quadratic eigenvalue complementarity problem over a general convex cone the solution of the conic quadratic eigenvalue complementarity problem cqeicp is first investigated without assuming symmetry on the matrices defining the problem a new sufficient condition for existence of solutions of cqeicp is presented extending to arbitrary pointed closed and convex cones a condition known to hold when the cone is the nonnegative orthant we also address the symmetric cqeicp where all its defining matrices are symmetric we show that assuming that two of its defining matrices are positive definite this symmetric cqeicp reduces to the computation of a stationary point of an appropriate merit function on a convex set furthermore we discuss the use of the so called spectral projected gradient spg algorithm for solving cqeicp when the cone of interest is the second order cone socqeicp a new algorithm is designed for the computation of the projections required by the spg method to deal with socqeicp numerical results are included to illustrate the efficiency of the spg method and the new projection technique in practice

the directional instability problem in systems with frictional contacts the research summarized in this paper addresses the directional instability of finite dimensional systems with unilateral frictional contacts conditions for the occurrence of this divergence type instability are discussed complementarity formulations are developed and numerical procedures are proposed for the solution of the corresponding non smooth stability eigenproblems various examples are analytically or numerically solved and discussed namely some finite element examples that have instability modes involving evolution towards slip or stick in different portions of the contact surface

on the finiteness of the cone spectrum of certain linear transformations on euclidean jordan algebras abstract let l be a linear transformation on a finite dimensional real hilbert space h and k be a closed convex cone with dual k in h the cone spectrum of l relative to k is the set of all real for which the linear complementarity problem x k y l x x k and x y 0 admits a nonzero solution x in the setting of a euclidean jordan algebra h and the corresponding symmetric cone k we discuss the finiteness of the cone spectrum for z transformations and quadratic representations on h

critical dynamics of the d 1 kinetic ising model the critical dynamics of the d 1 alternating bond glauber ising model and related models is studied there are two contributions to the critical slowing down one is due to the long range fluctuations near the critical point it is characterized by the dynamic exponent z 2 the other contribution is a temperature dependence of the bare time scale which is a result of short range phenomena in contrast to previous studies it is shown that all these models belong to one universality class

an adaptive detector for deterministic signals in noise of unknown spectra using the rao test an adaptive detector for a known deterministic signal of unknown amplitude in gaussian noise of unknown spectra is described the detector is based on the rao test which is asymptotically equivalent to the generalized likelihood ratio the detector achieves constant false alarm probability in the presence of large changes in input noise bandwidth and variance while providing optimum detection performance the results are supported by simulation

on eigenvalues induced by a cone constraint abstract let a be an n n real matrix and k r n be a closed convex cone the spectrum of a relative to k denoted by a k is the set of all r for which the linear complementarity problem x k ax x k x ax x 0 admitsa nonzero solution x r n the notation k stands for the positive dual cone of k the purpose of this work is to study the main properties of the mapping k and discuss some structural differences existing between the polyhedral case i e k is finitely generated and the nonpolyhedral case

on the invariance coincidence and statistical equivalence of the glrt rao test and wald test three common techniques to discriminate between alternatives in a binary hypothesis testing problem are the generalized likelihood ratio test glrt the rao test and the wald test in this paper we investigate some characteristics of the corresponding decision statistics and provide their expressions for some problems of particular interest in statistical signal processing first of all we focus on the invariance of the rao and wald tests with respect to transformations leaving the testing problem unaltered then we introduce necessary and sufficient conditions in order for their decision statistics to coincide with twice the logarithm of the glrt statistic finally we present some detection problems usually encountered in practical signal processing applications where the decision variables of the three quoted tests are equivalent namely related by strictly monotonic transformations

phase transitions on fractals ii sierpinski gaskets for pt i see ibid vol 16 p 1267 1983 the authors construct and investigate a family of fractals which are generalisations of the sierpinski gaskets sgs to all euclidean dimensionalities these fractal lattices have a finite order of ramification and can be considered marginal between one dimensional and higher dimensional geometries physical models defined on them are exactly solvable the authors argue that short range spin models on the sg show no finite temperature phase transitions as examples they solve a few spin models and study the resistor network and percolation problems on these lattices

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

smoothing functions for second order cone complementarity problems smoothing functions have been much studied in the solution of optimization and complementarity problems with nonnegativity constraints in this paper we extend smoothing functions to problems in which the nonnegative orthant is replaced by the direct product of second order cones these smoothing functions include the chen mangasarian class and the smoothed fischer burmeister function we study the lipschitzian and differential properties of these functions and in particular we derive computable formulas for these functions and their jacobians these properties and formulas can then be used to develop and analyze noninterior continuation methods for solving the corresponding optimization and complementarity problems in particular we establish the existence and uniqueness of the newton direction when the underlying mapping is monotone

second order cone programming second order cone programming socp problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the cartesian product of second order lorentz cones linear programs convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as socp problems as can many other problems that do not fall into these three categories these latter problems model applications from a broad range of fields from engineering control and finance to robust optimization and combinatorial optimization on the other hand semidefinite programming sdp that is the optimization problem over the intersection of an affine set and the cone of positive semidefinite matrices includes socp as a special case therefore socp falls between linear lp and quadratic qp programming and sdp like lp qp and sdp problems socp problems can be solved in polynomial time by interior point methods the computational effort per iteration required by these methods to solve socp problems is greater than that required to solve lp and qp problems but less than that required to solve sdp s of similar size and structure because the set of feasible solutions for an socp problem is not polyhedral as it is for lp and qp problems it is not readily apparent how to develop a simplex or simplex like method for socp while socp problems can be solved as sdp problems doing so is not advisable both on numerical grounds and computational complexity concerns for instance many of the problems presented in the survey paper of vandenberghe and boyd vb96 as examples of sdps can in fact be formulated as socps and should be solved as such in 2 3 below we give socp formulations for four of these examples the convex quadratically constrained quadratic programming qcqp problem problems involving fractional quadratic functions rutcor rutgers university e mail alizadeh rutcor rutgers edu research supported in part by the u s national science foundation grant ccr 9901991 ieor columbia university e mail gold ieor columbia edu research supported in part by the department of energy grant de fg02 92er25126 national science foundation grants dms 94 14438 cda 97 26385 and dms 01 04282

frequency domain cramer rao bound for gaussian processes an expression is derived for the asymptotic frequency domain cramer rao bound crb on the parameters of gaussian processes with information in their means the general result extends whittle s 1953 formula which is applicable to gaussian processes with information in their covariance matrices or spectra it is useful in many fields such as system identification radar and sonar examples of its application to system deconvolution and time delay estimation in colored noise are given

detection of broadband planewaves in the presence of gaussian noise of unknown covariance asymptotically optimum tests using the 2 d autoregressive noise model this paper addresses the problem of detecting a broadband planewave in noise of unknown spatial and temporal covariance at a linear array of sensors results of asymptotic detection theory are applied to derive detectors that approach optimal performance for large data records a parametric approach is used to model the statistics of the data a 2 d autoregressive 2dar model is chosen to model the noise process two broadband planewave signal models are considered both models represent the signal as a sum of monochromatic planewaves in the gaussian model the amplitudes are assumed to be gaussian with a single variance parameter whereas in the deterministic assumption they are individual unknown parameters detectors based on asymptotic theory are derived for both models as part of the development of the asymptotically as optimum detector the fisher information matrix fim is derived a proof of the locally asymptotic normal lan property is provided for the gaussian model probability density function pdf both detectors however are as equivalent to the generalized likelihood ratio test glrt are as of constant false alarm rate cfar and perform as as well as the glrt constructed with full knowledge of the noise statistics the performance of both detectors are compared with each other and to a standard spatially normalized beamformer in a computer simulation

motzkin decomposition of closed convex sets via truncation this work has been supported by the micinn of spain grants mtm2011 29064 c03 01 02 by the barcelona graduate school of economics by the government of catalonia by conacyt of mexico grant 55681 and by cnpq of brazil grant 301280 86 the first author is partner investigator in the australian research council discovery project dp120100467 the third author is affiliated tomove markets organizations and votes in economics

critical dynamics of the alternating bond kinetic ising model the critical dynamics of the alternating bond kinetic ising model on a chain is examined it is shown that previous nonuniversal results for the dynamical critical exponent z for single spin flip dynamics should be reinterpreted the critical slowing down is due to two distinct contributions which when separated indicate that the value of z is universal the exponent remains universal even when two spin flip dynamics are considered

projected barzilai borwein methods for large scale box constrained quadratic programming this paper studies projected barzilai borwein pbb methods for large scale box constrained quadratic programming recent work on this method has modified the pbb method by incorporating the grippo lampariello lucidi gll nonmonotone line search so as to enable global convergence to be proved we show by many numerical experiments that the performance of the pbb method deteriorates if the gll line search is used we have therefore considered the question of whether the unmodified method is globally convergent which we show not to be the case by exhibiting a counter example in which the method cycles a new projected gradient method pabb is then considered that alternately uses the two barzilai borwein steplengths we also give an example in which this method may cycle although its practical performance is seen to be superior to the pbb method with the aim of both ensuring global convergence and preserving the good numerical performance of the unmodified methods we examine other recent work on nonmonotone line searches and propose a new adaptive variant with some attractive features further numerical experiments show that the pabb method with the adaptive line search is the best bb like method in the positive definite case and it compares reasonably well against the gpcg algorithm of more and toraldo in the indefinite case the pbb method with the adaptive line search is shown on some examples to find local minima with better solution values and hence may be preferred for this reason

critical dynamics and universality in kinetic ising models without translational invariance the critical dynamics of the glauber ising model on nontranslationally invariant lattices is studied both a quasi periodic and a fractal geometry are considered the distribution of inverse relaxation times rho 1 tau is calculated using a generating function method the distribution consists of bands with an internal self similar structure in the limit 1 tau to 0 rho 1 tau diverges with a universal exponent related to the dynamic critical exponent z the width of the lowest frequency band is determined by a nonuniversal bare time scale which is related to the presence of metastable states