robust stabilization of interval plants using lead or lag compensators abstract a lead or lag compensator robustly stabilizes a family of interval plants if and only if it simultaneously stabilizes the vertex plants

submodular functions from discrete to continous domains submodular set functions have many applications in combinatorial optimization as they can be minimized and approximately maximized in polynomial time a key element in many of the algorithms and analyses is the possibility of extending the submodular set function to a convex function which opens up tools from convex optimization submodularity goes beyond set functions and has naturally been considered for problems with multiple labels or for functions defined on continuous domains where it corresponds essentially to cross second derivatives being nonpositive in this paper we show that most results relating submodularity and convexity for set functions can be extended to all submodular functions in particular a we naturally define a continuous extension in a set of probability measures b show that the extension is convex if and only if the original function is submodular c prove that the problem of minimizing a submodular function is equivalent to a typically non smooth convex optimization problem and d propose another convex optimization problem with better computational properties e g a smooth dual problem most of these extensions from the set function situation are obtained by drawing links with the theory of multi marginal optimal transport which provides also a new interpretation of existing results for set functions we then provide practical algorithms to minimize generic submodular functions on discrete domains with associated convergence rates

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

locally monotonic regression the concept of local monotonicity appears in the study of the set of root signals of the median filter and provides a measure of the smoothness of the signal the median filter is a suboptimal smoother under this measure of smoothness since a filter pass does necessarily yield a locally monotonic output even if a locally monotonic output does result there is no guarantee that it will possess other desirable properties such as optimal similarity to the original signal locally monotonic regression is a technique for the optimal smoothing of finite length discrete real signals under such a criterion a theoretical framework in which the existence of locally monotonic regression is proved and algorithms for their computation are given regression is considered as an approximation problem in r sub n the criterion of approximation is derived from a semimetric and the approximating set is the collection of signals sharing the property of being locally monotonic

mathematical programming algorithms for regression based nonlinear filtering in r sup n this paper is concerned with regression under a sum of partial order constraints examples include locally monotonic piecewise monotonic runlength constrained and unimodal and oligomodal regression these are of interest not only in nonlinear filtering but also in density estimation and chromatographic analysis it is shown that under a least absolute error criterion these problems can be transformed into appropriate finite problems which can then be efficiently solved via dynamic programming techniques although the result does not carry over to least squares regression hybrid programming algorithms can be developed to solve least squares counterparts of certain problems in the class

minimizing separable convex functions subject to simple chain constraints minimizing a separable convex objective subject to an ordering restriction on its variables is a generalization of a class of problems in statistical estimation and inventory control it is shown that a pool adjacent violators pav algorithm can be used to compute an optimal solution of this problem as well as the minimal and maximal extended solutions which provide lower and upper bounds on all optimal solutions and solve certain subproblems these results unify and extend several previously known results in addition it is shown that a pav algorithm can be applied to solving the problem with integer constraints on the variables

a fast scaling algorithm for minimizing separable convex functions subject to chain constraints we consider the problem of minimizing j nc j x j subject to the following chain constraints x 1 x 2 x 3 x n where c j x j is a convex function of x j for each j n 1 2 n this problem is a generalization of theisotonic regression problems with complete order an important class of problems in regression analysis that has been examined extensively in the literature we refer to this problem as thegeneralized isotonic regression problem in this paper we focus on developing a fast scaling algorithm to obtain an integer solution of the generalized isotonic regression problem letu denote the difference between an upper bound on an optimal value of x n and a lower bound on an optimal value of x 1 under the assumption that the evaluation of any function c j x j takeso 1 time we show that the generalized isotonic regression problem can be solved ino n logu time this improves by a factor of n the previous best running time ofo n 2 logu to solve the same problem in addition when our algorithm is specialized to theisotonic median regression problem where c j x j c j x j a ji for specified values ofc js anda js the algorithm obtains a real valued optimal solution ino n logn time this time bound matches the best available time bound to solve the isotonic median regression problem but our algorithm uses simpler data structures and may be easier to implement

blind deconvolution using a variational approach to parameter image and blur estimation following the hierarchical bayesian framework for blind deconvolution problems in this paper we propose the use of simultaneous autoregressions as prior distributions for both the image and blur and gamma distributions for the unknown parameters hyperparameters of the priors and the image formation noise we show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations we apply variational methods to approximate the posterior probability of the unknown image blur and hyperparameters and propose two different approximations of the posterior distribution one of these approximations coincides with a classical blind deconvolution method the proposed algorithms are tested experimentally and compared with existing blind deconvolution methods

optimal estimation of deterioration from diagnostic image sequence estimation of mechanical structure damage can greatly benefit from the knowledge that the damage accumulates irreversibly over time this paper formulates a problem of estimation of a pixel wise monotonic increasing or decreasing time series of images from noisy blurred image data our formulation includes temporal monotonicity constraints and a spatial regularization penalty we cast the estimation problem as a large scale quadratic programming qp optimization and describe an efficient interior point method for solving this problem the method exploits the special structure of the qp and scales well to problems with more than a million of decision variables and constraints the proposed estimation approach performs well for simulated data we demonstrate an application of the approach to diagnostic images obtained in structural health monitoring experiments and show that it provides a good estimate of the damage accumulation trend while suppressing spatial and temporal noises

robust output tracking control of siso plants with multiple operating points and with parametric and unstructured uncertainties the robust output tracking control problem is considered for single input single output plants with multiple operating points and with both parametric and unstructured uncertainties i e interval parameter uncertainties and norm bounded unmodelled dynamics the parametric uncertainties can involve parameter perturbations as well as degree variations the plant with uncertainties is assumed to be of minimum phase but is not required to have a fixed number of unstable poles a new method is presented by which a linear time invariant robust controller is designed in two steps first a nominal controller is designed to get exact output tracking for the nominal plant then a robust compensator is added to achieve robust properties it is shown that robust stability robust static state property robust transient property and robust tracking property can be achieved simultaneously a computationally tractable design procedure is presented a salient feature of our results shown in the present paper is th

computing the frequency response of linear systems with parametric perturbation abstract the problem of computing the frequency response of linear systems with parametric perturbation is addressed under the assumption that the coefficients of the system transfer function depend on the perturbation parameters in a linear manner we provide results for plotting the frequency response of the perturbed transfer function these results are useful in determining the h norm gain margin and phase margin and in improving the diagonal dominance of multi input multi out put uncertain systems an illustrative example is provided to demonstrate the results

the min max algorithm and isotonic regression there is growing interest in statistical inference under order restrictions a major demand in this subject is to have a fast direct method to solve the least squares problem of partially ordered isotonic regression the min max algorithm is such a method in which the user searches for the global minimum and the local maximum successively a comparison of algorithms for partially ordered isotonic regression is included as an application using this efficient algorithm it is feasible to approximate critical values of isotonic tests by simulation

an interior point method for large scale l 1 regularized logistic regression logistic regression with l1 regularization has been proposed as a promising method for feature selection in classification problems in this paper we describe an efficient interior point method for solving large scale l1 regularized logistic regression problems small problems with up to a thousand or so features and examples can be solved in seconds on a pc medium sized problems with tens of thousands of features and examples can be solved in tens of seconds assuming some sparsity in the data a variation on the basic method that uses a preconditioned conjugate gradient method to compute the search step can solve very large problems with a million features and examples e g the 20 newsgroups data set in a few minutes on a pc using warm start techniques a good approximation of the entire regularization path can be computed much more efficiently than by solving a family of problems independently

suboptimal receding horizon estimation via noise blocking abstract for discrete time linear systems we propose a suboptimal approach to constrained estimation so that the associated computation burden is reduced this is achieved by enforcing a move blocking mb structure in the estimated process noise sequence pns we show that full information estimation fie and receding horizon estimation rhe with mb are both stable in the sense of an observer the techniques in proving stability are inspired by those that have been proposed for standard rhe to be specific stability results are mainly achieved by i carefully embellishing the general assumptions for standard rhe to accommodate the mb requirement ii exploiting the principle of optimality as well as convexity of the quadratic programs qps associated with fie and rhe iii relying on the fact that the kalman filter is the best linear estimator in the least squares sense a crucial requirement in achieving stability for mb rhe is that the segment structure ss of the pns of mb fie for the optimization steps within the receding horizon i e steps between t n and t 1 has to be enforced in the mb rhe optimization as a result the mb rhe strategy becomes a dynamic estimator with a periodically varying computational complexity the theoretical results have been illustrated with examples

on the nyquist envelope of an interval plant family in this note we study the envelope of the nyquist plots generated by an interval plant family and show that this boundary is not always contained in the nyquist plots of the kharitonov plants with this motivation in mind we give a sufficient condition for an envelope point to be contained in the nyquist plot of a kharitonov plant and use it to generate large and critical portions of the nyquist envelope e g we show that the outer nyquist envelope of a stable interval plant is generated by the nyquist plots of the kharitonov plants another by product of this sufficient condition is a framework for developing new extreme point results for interval feedback systems this framework is useful in computing the phase margin and the maximal peaking in the sensitivity and complementary sensitivity functions and in stating a robust version of the circle criterion we also use this framework to easily explain existing extreme point results for the gain margin the h sub spl infin norm and the positive realness of interval plants one conclusion which emerges is this seemingly all important properties of an interval feedback system are deducible from the kharitonov plants

extreme point results for robust stabilization of interval plants with first order compensators it has been shown previously that a first order compensator robustly stabilizes an internal plant family if and only if it stabilizes all of the extreme plants these extreme plants are obtained by considering all possible combinations for the extreme values of the numerator and denominator coefficients in this work the authors prove a stronger result namely that it is necessary and sufficient to stabilize only sixteen of the extreme plants these sixteen plants are generated using the kharitonov polynomials associated with the numerator and denominator furthermore when additional information about the compensator is specified sign of the gain and signs and relative magnitudes of the pole and zero then in some cases it is necessary and sufficient to stabilize eight critical plants while in other cases it is necessary and sufficient to stabilize twelve critical plants

linearizability of three families of cubic systems we obtain the necessary and sufficient conditions for linearizability isochronicity of three families of eight parametric cubic systems this completes the classification of the linearizable systems studied by romanovski and robnik 2001 j phys a math gen 34 10267 92

investigation of robust stability of fractional order multilinear affine systems 2q convex parpolygon approach abstract this paper discusses the robust stability problem of fractional order systems with the multi linear affine uncertainty structure the 2 q convex parpolygon approach has been extended to compute the value set of the fractional order uncertain system and to investigate the robust stability via zero exclusion principle an illustrative example is included for fractional order multi linear affine system to present the advantages of the 2 q convex parpolygon approach over classical value set computation methods in the stability investigation

exact complexity certification of active set methods for quadratic programming active set methods are recognized to often outperform other methods in terms of speed and solution accuracy when solving small size quadratic programming qp problems making them very attractive in embedded linear model predictive control mpc applications a drawback of active set methods is the lack of tight bounds on the worst case number of iterations a fundamental requirement for their implementation in a real time system extensive simulation campaigns provide an indication of the expected worst case computation load but not a complete guarantee this paper solves such a certification problem by proposing an algorithm to compute the exact bound on the maximum number of iterations and floating point operations required by a state of the art dual active set qp solver the algorithm is applicable to a given qp problem whose linear term of the cost function and right hand side of the constraints depend linearly on a vector of parameters as in the case of linear mpc in addition a new solver is presented that combines explicit and implicit mpc ideas guaranteeing improvements of the worst case computation time the ability of the approach to exactly quantify memory and worst case computation requirements is tested on a few mpc examples also highlighting when online optimization should be preferred to explicit mpc

an efficient algorithm for image segmentation markov random fields and related problems problems of statistical inference involve the adjustment of sample observations so they fit some a priori rank requirements or order constraints in such problems the objective is to minimize the deviation cost function that depends on the distance between the observed value and the modify value in markov random field problems there is also a pairwise relationship between the objects the objective in markov random field problem is to minimize the sum of the deviation cost function and a penalty function that grows with the distance between the values of related pairs separation function we discuss markov random fields problems in the context of a representative application the image segmentation problem in this problem the goal is to modify color shades assigned to pixels of an image so that the penalty function consisting of one term due to the deviation from the initial color shade and a second term that penalizes differences in assigned values to neighboring pixels is minimized we present here an algorithm that solves the problem in polynomial time when the deviation function is convex and separation function is linear and in strongly polynomial time when the deviation cost function is linear quadratic or piecewise linear convex with few pieces where few means a number exponential in a polynomial function of the number of variables and constraints the complexity of the algorithm for a problem on n pixels or variables m adjacency relations or constraints and range of variable values colors u is o t n m n log u where t n m is the complexity of solving the minimum s t cut problem on a graph with n nodes and m arcs furthermore other algorithms are shown to solve the problem with convex deviation and convex separation in running time o mn log n log nu and the problem with nonconvex deviation and convex separation in running time o t nu mu the nonconvex separation problem is np hard even for fixed value of u for the family of problems with convex deviation functions and linear separation function the algorithm described here runs in polynomial time which is demonstrated to be fastest possible

on the statistical optimality of locally monotonic regression locally monotonic regression is a recently proposed technique for the deterministic smoothing of finite length discrete signals under the smoothing criterion of local monotonicity locally monotonic regression falls within a general framework for the processing of signals that may be characterized in three ways regressions are given by projections that are determined by semimetrics the processed signals meet shape constraints that are defined at the local level and the projections are optimal statistical estimates in the maximum likelihood sense the authors explore the relationship between the geometric and deterministic concept of projection onto generally nonconvex sets and the statistical concept of likelihood with the object of characterizing projections under the family of the p semi metrics as maximum likelihood estimates of signals contaminated with noise from a well known family of exponential densities

isotonic regression and isotonic projection abstract the note describes the cones in the euclidean space admitting isotonic metric projection with respect to the coordinate wise ordering as a consequence it is shown that the metric projection onto the isotonic regression cone the cone defined by the general isotonic regression problem admits a projection which is isotonic with respect to the coordinate wise ordering

iterative image restoration using approximate inverse preconditioning removing a linear shift invariant blur from a signal or image can be accomplished by inverse or wiener filtering or by an iterative least squares deblurring procedure because of the ill posed characteristics of the deconvolution problem in the presence of noise filtering methods often yield poor results on the other hand iterative methods often suffer from slow convergence at high spatial frequencies this paper concerns solving deconvolution problems for atmospherically blurred images by the preconditioned conjugate gradient algorithm where a new approximate inverse preconditioner is used to increase the rate of convergence theoretical results are established to show that fast convergence can be expected and test results are reported for a ground based astronomical imaging problem

technical note a polynomial simplex method for the assignment problem we present a polynomial primal simplex algorithm for the assignment problem for n n assignment problem with integer cost coefficients the algorithm generates at most n3 ln bases prior to reach the optimal basis where is the difference in objective value between an initial extreme point and the optimal extreme point

a sparse counterpart of reichel and gragg s package qrup we describe how to maintain the triangular factor of a sparse qr factorization when columns are added and deleted and q cannot be stored for sparsity reasons the updating procedures could be thought of as a sparse counterpart of reichel and gragg s package qrup they allow us to solve a sequence of sparse linear least squares subproblems in which each matrix b k is an independent subset of the columns of a fixed matrix a and b k 1 is obtained by adding or deleting one column like coleman and hulbert t coleman l hulbert a direct active set algorithm for large sparse quadratic programs with simple bounds math program 45 1989 373 406 we adapt the sparse direct methodology of bjorck and oreborn of the late 1980s but without forming a ta which may be only positive semidefinite our matlab 5 implementation works with a suitable row and column numbering within a static triangular sparsity pattern that is computed in advance by symbolic factorization of a ta and preserved with placeholders

a 98 effective lot sizing rule for a multi product multi stage production inventory system we study a multi product multi stage production inventory system in continuous time in process and finished goods are referred to as products and inventories of a single item held at different locations are treated as different products external demand can occur for any or all of the products at a constant product dependent rate when an order is placed for a product it is instantly delivered the set up cost is a function of the set of products being ordered at that point in time the goal is to schedule orders for each of the products over an infinite horizon so as to minimize the long run average cost we define a new class of policies in which each product uses a stationary interval of time between successive orders and the ratio of the order intervals of any two products is an integer power of two we show that there is always a policy in this class that is within 2 of optimal this extends a similar result for the one warehouse multi retailer system for assembly systems we show how to compute such a policy in 0n log n time for general systems a sequence of max flow min cut computations is required the algorithm is efficient for very large systems

a non parametric approach to extending generic binary classifiers for multi classification ensemble methods which combine generic binary classifier scores to generate a multi classification output are commonly used in state of the art computer vision and pattern recognition systems that rely on multi classification in particular we consider the one vs one decomposition of the multi class problem where binary classifier models are trained to discriminate every class pair we describe a robust multi classification pipeline which at a high level involves projecting binary classifier scores into compact orthogonal subspaces followed by a non linear probabilistic multi classification step using kernel density estimation kde we compare our approach against state of the art ensemble methods dcs drcw on 16 multi class datasets we also compare against the most commonly used ensemble methods vote nest on 6 real world computer vision datasets finally we measure the statistical significance of our approach using non parametric tests experimental results show that our approach gives a statistically significant improvement in multi classification performance over state of the art highlightsensemble methods combine binary classifiers to yield a multi classification output one vs one ensemble binary classifiers trained to discriminate each class pair we propose a robust non parametric probabilistic one vs one ensemble method kdemrp kdemrp improves classification performance over state of the art dcs drcw kdemrp improvements are statistically significant

linearizability conditions for lotka volterra planar complex cubic systems in this paper we investigate the linearizability problem for the two dimensional planar complex system the necessary and sufficient conditions for the linearizability of this system are found from them the conditions for isochronicity of the corresponding real system can be derived

a general interactive framework for false discovery rate control under structural constraints we propose a general framework based on selectively traversed accumulation rules star for interactive multiple testing with generic structural constraints on the rejection set it combines accumulation tests from ordered multiple testing with data carving ideas from post selection inference allowing for highly flexible adaptation to generic structural information our procedure defines an interactive protocol for gradually pruning a candidate rejection set beginning with the set of all hypotheses and shrinking with each step by restricting the information at each step via a technique we call masking our protocol enables interaction while controlling the false discovery rate fdr in finite samples for any data adaptive update rule that the analyst may choose we suggest update rules for a variety of applications with complex structural constraints show that star performs well for problems ranging from convex region detection to fdr control on directed acyclic graphs and show how to extend it to regression problems where knockoff statistics are available in lieu of p values

a primal dual potential reduction method for problems involving matrix inequalities we describe a potential reduction method for convex optimization problems involving matrix inequalities the method is based on the theory developed by nesterov and nemirovsky and generalizes gonzaga and todd s method for linear programming a worst case analysis shows that the number of iterations grows as the square root of the problem size but in practice it appears to grow more slowly as in other interior point methods the overall computational effort is therefore dominated by the least squares system that taust be solved in each iteration a type of conjugate gradient algorithm can be used for this purpose which results in important savings for two reasons first it allows us to take advantage of the special structure the problems often have e g lyapunov or algebraic riccati inequalities second we show that the polynomial bound on the number ofiterations remains valid even if the conjugate gradient algorithm is not run until completion which in practice can greatly reduce the computational effort per iteration we describe in detail how the algorithm works for optimization problems with l lyapunov inequaliues each of size m we prove an overall worst case operation count of o mssll5 the average case complexity appears to be closer to o m4ll5 this estimate is justified by extensive numerical experimentation and is consistent with other researchers experience with the practical performance of interior point algorithms for linear programming this result means that the computational cost of extending current control theory based on the solution of lyapunov or riccati equations to a theory that is based on the solution of multiple coupled lyapunov or riccati inequalities is modest

on robust stability of interval control systems the authors develop results on the robust stability of a nonlinear control system containing both parametric as well as unstructured uncertainty the basic system considered is that of the classical lur e problem of nonlinear control theory a robust version of the lur e problem consisting of a family of linear time invariant systems subjected simultaneously to bounded parameter variations and feedback perturbations from a family of sector bounded nonlinear gains is presently treated by using the kharitonov theorem to develop some extremal results on positive realness of interval transfer functions i e a family of rational transfer functions with bounded independent coefficient perturbations the authors determine the size of a sector of nonlinear feedback gains for which absolute stability can be guaranteed these calculations amount to the determination of the stability margin of the system under joint parametric and nonlinear feedback perturbations

vertex results for parametric h problems of weighted interval feedback systems abstract this paper deals with the parametric h problems of weighted interval feedback systems it will be shown by an example that the maximal h norm of the first order weighted sensitivity function does not enjoy the extremality property generally but it is achieved at one of the 16 edge plants and this result can be generalized to the case of some high order weighting functions the conditions under which vertex results hold will be investigated finally

the centre and isochronicity problems for some cubic systems we present an efficient method for computing focus and linearizability quantities of polynomial differential equation systems we apply the method to computing these quantities for ten eight parametric cubic systems and obtain the necessary and sufficient conditions of linearizability isochronicity of these systems we also show that there is a kind of duality between the problem of constructing algebraic invariant curves first integrals and linearizing transformations on one side and the problem of solving some first order linear partial differential equations on the other side

active set algorithms for isotonic regression a unifying framework in this and subsequent papers we will show that several algorithms for the isotonic regression problem may be viewed as active set methods the active set approach provides a unifying framework for studying algorithms for isotonic regression simplifies the exposition of existing algorithms and leads to several new efficient algorithms we also investigate the computational complexity of several algorithms

h sub 2 norm checking for systems with parameter uncertainties this paper studies the problem of h sub 2 norm checking for a mimo system with parameter uncertainties under the assumptions that the coefficients of the numerator polynomial of the system s transfer function are multi affine functions of the uncertain parameter that varies in a convex polytope and that the coefficients of the denominator polynomial of the system s transfer function are affine functions of the uncertain parameter which varies in a convex polytope a vertex checking result is obtained

equivalence of some quadratic programming algorithms we formulate a general algorithm for the solution of a convex but not strictly convex quadratic programming problem conditions are given under which the iterates of the algorithm are uniquely determined the quadratic programming algorithms of fletcher gill and murray best and ritter and van de panne and whinston dantzig are shown to be special cases and consequently are equivalent in the sense that they construct identical sequences of points the various methods are shown to differ only in the manner in which they solve the linear equations expressing the kuhn tucker system for the associated equality constrained subproblems equivalence results have been established by goldfarb and djang for the positive definite hessian case our analysis extends these results to the positive semi definite case

interior point methodology for 3 d pet reconstruction interior point methods have been successfully applied to a wide variety of linear and nonlinear programming applications this paper presents a class of algorithms based on path following interior point methodology for performing regularized maximum likelihood ml reconstructions on three dimensional 3 d emission tomography data the algorithms solve a sequence of subproblems that converge to the regularized maximum likelihood solution from the interior of the feasible region the nonnegative orthant the authors propose two methods a primal method which updates only the primal image variables and a primal dual method which simultaneously updates the primal variables and the lagrange multipliers a parallel implementation permits the interior point methods to scale to very large reconstruction problems termination is based on well defined convergence measures namely the karush kuhn tucker first order necessary conditions for optimality the authors demonstrate the rapid convergence of the path following interior point methods using both data from a small animal scanner and monte carlo simulated data the proposed methods can readily be applied to solve the regularized weighted least squares reconstruction problem

robust stability under structured and unstructured perturbations the problem of robust stability for linear time invariant single output control systems subject to both structured parametric and unstructured h sub infinity perturbations is studied a generalization of the small gain theorem which yields necessary and sufficient conditions for robust stability of a linear time invariant dynamic system under perturbations of mixed type is presented the solution involves calculating the h sub infinity norm of a finite number of extremal plants the problem of calculating the exact structured and unstructured stability margins is then constructively solved a feedback control system containing a linear time invariant plant which is subject to both structured and unstructured perturbations is considered the case where the system to be controlled is interval is treated and a nonconservative easily verifiable necessary and sufficient condition for robust stability is given the solution is based on the extremal of a finite number of line segments in the plant parameter property of a finite number of line segments in the plant parameter space along which the points closest to instability are encountered

establishing consistent and realistic reorder intervals in production distribution systems the objective of this paper is to present a model and algorithm that can be used to find consistent and realistic reorder intervals for each item in large scale production distribution systems we assume such systems can be represented by directed acyclic graphs demand for each end item is assumed to occur at a constant and continuous rate production is instantaneous and no backorders are allowed both fixed setup costs and echelon holding costs are charged at each stage we limit our attention to nested and stationary policies furthermore we restrict the reorder interval for each stage to be a power of 2 times a base planning period the model that results from these assumptions is an integer nonlinear programming problem the optimal solution can be found using the proposed algorithm which is a polynomial time algorithm a real world example is given to illustrate the procedure

efficient minimization methods of mixed l 2 l 1 and l 1 l 1 norms for image restoration image restoration problems are often solved by finding the minimizer of a suitable objective function usually this function consists of a data fitting term and a regularization term for the least squares solution both the data fitting and the regularization terms are in the ell 2 norm in this paper we consider the least absolute deviation lad solution and the least mixed norm lmn solution for the lad solution both the data fitting and the regularization terms are in the ell 1 norm for the lmn solution the regularization term is in the ell 1 norm but the data fitting term is in the ell 2 norm since images often have nonnegative intensity values the proposed algorithms provide the option of taking into account the nonnegativity constraint the lmn and lad solutions are formulated as the solution to a linear or quadratic programming problem which is solved by interior point methods at each iteration of the interior point method a structured linear system must be solved the preconditioned conjugate gradient method with factorized sparse inverse preconditioners is employed to solve such structured inner systems experimental results are used to demonstrate the effectiveness of our approach we also show the quality of the restored images using the minimization of mixed ell 2 ell 1 and ell1 ell 1 norms is better than that using only the ell 2 norm

diffuse prior monotonic likelihood ratio test for evaluation of fused image quality measures this paper introduces a novel method to score how well proposed fused image quality measures fiqms indicate the effectiveness of humans to detect targets in fused imagery the human detection performance is measured via human perception experiments a good fiqm should relate to perception results in a monotonic fashion the method computes a new diffuse prior monotonic likelihood ratio dpmlr to facilitate the comparison of the h1 hypothesis that the intrinsic human detection performance is related to the fiqm via a monotonic function against the null hypothesis that the detection and image quality relationship is random the paper discusses many interesting properties of the dpmlr and demonstrates the effectiveness of the dpmlr test via monte carlo simulations finally the dpmlr is used to score fiqms with test cases considering over 35 scenes and various image fusion algorithms

contrast invariant snr and isotonic regressions we design an image quality measure independent of contrast changes which are defined as a set of transformations preserving an order between the level lines of an image this problem can be expressed as an isotonic regression problem depending on the definition of a level line the partial order between adjacent regions can be defined through chains polytrees or directed acyclic graphs we provide a few analytic properties of the minimizers and design original optimization procedures together with a full complexity analysis the methods worst case complexities range from o n for chains to o n log n for polytrees and o frac n 2 sqrt epsilon for directed acyclic graphs where n is the number of pixels and epsilon is a relative precision the proposed algorithms have potential applications in change detection stereo vision image registration color image processing or image fusion a c implementation with matlab headers is available at https github com pierre weiss contrast invariant snr

some new results on the simultaneous stabilizability of a family of single input single output systems abstract in this paper we obtain sufficiency conditions on the problem of simultaneous stabilization of a parameterized family of single input single output plants by a non switching compensator the sufficiency conditions include simultaneous stabilization and simultaneous pole assignment of a finite number of plants

distributed control of spatially reversible interconnected systems with boundary conditions we present a class of spatially interconnected systems with boundary conditions that have close links with their spatially invariant extensions in particular well posedness stability and performance of the extension imply the same characteristics for the actual finite extent system in turn existing synthesis methods for control of spatially invariant systems can be extended to this class the relation between the two kinds of systems is proved using ideas based on the method of images of partial differential equations theory and uses symmetry properties of the interconnection as a key tool

random distortion testing and optimality of thresholding tests this paper addresses the problem of testing whether the mahalanobis distance between a random signal and a known deterministic model 0 exceeds some given non negative real number or not when has unknown probability distribution and is observed in additive independent gaussian noise with positive definite covariance matrix when is deterministic unknown we prove the existence of thresholding tests on the mahalanobis distance to 0 that have specified level and maximal constant power mcp the mcp property is a new optimality criterion involving wald s notion of tests with uniformly best constant power ubcp on ellipsoids for testing the mean of a normal distribution when the signal is random with unknown distribution constant power maximality extends to maximal constant conditional power mccp and the thresholding tests on the mahalanobis distance to 0 still verify this novel optimality property our results apply to the detection of signals in independent and additive gaussian noise in particular for a large class of possible model mismatches mccp tests can guarantee a specified false alarm probability in contrast to standard neyman pearson tests that may not respect this constraint

synergy of monotonic rules this article describes a method for constructing a special rule we call it synergy rule that uses as its input information the outputs scores of several monotonic rules which solve the same pattern recognition problem as an example of scores of such monotonic rules we consider here scores of svm classifiers in order to construct the optimal synergy rule we estimate the conditional probability function based on the direct problem setting which requires solving a fredholm integral equation generally solving a fredholm equation is an ill posed problem however in our model we look for the solution of the equation in the set of monotonic and bounded functions which makes the problem well posed this allows us to solve the equation accurately even with training data sets of limited size in order to construct a monotonic solution we use the set of functions that belong to reproducing kernel hilbert space rkhs associated with the ink spline kernel splines with infinite numbers of knots of degree zero the paper provides details of the methods for finding multidimensional conditional probability in a set of monotonic functions to obtain the corresponding synergy rules we demonstrate effectiveness of such rules for 1 solving standard pattern recognition problems 2 constructing multi class classification rules 3 constructing a method for knowledge transfer from multiple intelligent teachers in the lupi paradigm

block bialternate sum and associated stability formulae abstract a new block bialternate sum of a partitioned square matrix with itself is defined and some basic properties established it has similar properties to the bialternate sum but it preserves the block structure of the summand it is used in place of the block kronecker sum and the block lyapunov sum to solve maximal stability problems of stable systems under low gain integral control and of singularly perturbed systems it is also used to find the critical gains for a first order controller with a scalar plant from which all stabilizing first order controllers can be constructed in each stability problem the internal dimensions of the resulting closed formulae are lower than those currently available

a competitive dual simplex method for the assignment problem where there is abundance of mystery and confusion in every direction the truth seldom remains hidden for long it s a matter of having plenty of angles to go at it from only the utterly simple crimes the simplex crimes you may say have the trick of remaining baffling sir john from michael innes the open house a sir john appleby mystery penguin books 1974

a geometrical approach to iterative isotone regression in the present paper we propose and analyze a novel method for estimating a univariate regression function of bounded variation the underpinning idea is to combine two classical tools in nonparametric statistics namely isotonic regression and the estimation of additive models a geometrical interpretation enables us to link this iterative method with von neumann s algorithm moreover making a connection with the general property of isotonicity of projection onto convex cones we derive another equivalent algorithm and go further in the analysis

monotonic regression a new way for correlating subjective and objective ratings in image quality research to assess the performance of image quality metrics iqms some regressions such as logistic regression and polynomial regression are used to correlate objective ratings with subjective scores however some defects in optimality are shown in these regressions in this correspondence monotonic regression mr is found to be an effective correlation method in the performance assessment of iqms both theoretical analysis and experimental results have proven that mr performs better than any other regression we believe that mr could be an effective tool for performance assessment in the iqm research

distributed control design for spatially interconnected systems this paper deals with analysis synthesis and implementation of distributed controllers designed for spatially interconnected systems we develop a state space framework for posing problems of this type and focus on systems whose model is spatially discrete in this paper analysis and synthesis results are developed for this class of systems using the l sub 2 induced norm as the performance criterion the results are stated in terms of linear matrix inequalities and are thus readily amenable to computation a special implementation of the resulting controllers is presented which is particularly attractive for distributed operation of the controller several examples are provided to further illustrate the application of the results

algorithmic derivation of isochronicity conditions abstract this paper is concerned with obtaining the conditions under which the origin is an isochronous centre for certain planar polynomial systems the necessity of these conditions is proved using a computer implementation of an algorithm first proposed by i i pleshkan their sufficiency is then proved using various methods

technical communique a note on absolute stability of uncertain systems the absolute stability of nonlinear systems is an important robustness issue which has been studied intensively since its first formulation by lur e recently extensions of the solutions to different versions of this problem have been developed for cases with either structured or unstructured uncertainties in the linear part in this note the circle criterion and the popov criterion are recast in an even more general setting one which accommodates both types of perturbations in the linear plant numerical examples are provided to illustrate the application of these frequency domain tools

computation of the frequency response of multilinear affine systems deals with the problem of computing the frequency response of an uncertain transfer function whose numerator and denominator polynomials are multiples of independent uncertain polynomials of the form p s q l sub o q l sub 1 q s spl middot spl middot spl middot l sub n q s sup n whose coefficients depend linearly on q q sub 1 q sub 2 q sub q sup t and the uncertainty box is q q q sub i spl epsiv q sub i q sub i i 1 2 q using the geometric structure of the value set of p s q a powerful edge elimination procedure is proposed for computing the bode nyquist and nichols envelopes of these uncertain systems a numerical example is included to illustrate the benefit of the method presented