theoretical analysis and performance of ofdm signals in nonlinear awgn channels orthogonal frequency division multiplexing ofdm baseband signals may be modeled by complex gaussian processes with rayleigh envelope distribution and uniform phase distribution if the number of carriers is sufficiently large the output correlation function of instantaneous nonlinear amplifiers and the signal to distortion ratio can be derived and expressed in an easy way as a consequence the output spectrum and the bit error rate ber performance of ofdm systems in nonlinear additive white gaussian noise channels are predictable both for uncompensated amplitude modulation amplitude modulation am am and amplitude modulation pulse modulation am pm distortions and for ideal predistortion the aim of this work is to obtain the analytical expressions for the output correlation function of a nonlinear device and for the ber performance the results in closed form solutions are derived for am am and am pm curves approximated by bessel series expansion and for the ideal predistortion case

on the distribution of the peak to average power ratio in ofdm signals the distribution of the peak to average power ratio papr in strictly band limited orthogonal frequency division multiplexing ofdm signals is studied assuming that the base band ofdm signal is characterized as a band limited complex gaussian process we first attempt to derive the exact distribution of the papr in the band limited ofdm signals since this distribution cannot be expressed in a closed form we further develop a simple closed form approximation based on the level crossing rate analysis comparisons of the proposed distributions with those obtained by computer simulations show good agreement and convergence with an increase in the number of subcarriers

entropy like proximal methods in convex programming we study an extension of the proximal method for convex programming where the quadratic regularization kernel is substituted by a class of convex statistical distances called divergences which are typically entropy like in form after establishing several basic properties of these quasi distances we present a convergence analysis of the resulting entropy like proximal algorithm applying this algorithm to the dual of a convex program we recover a wide class of nonquadratic multiplier methods and prove their convergence

an interior proximal method in vector optimization abstract this paper studies the vector optimization problem of finding weakly efficient points for maps from r n to r m with respect to the partial order induced by a closed convex and pointed cone c r m with nonempty interior we develop for this problem an extension of the proximal point method for scalar valued convex optimization problem with a modified convergence sensing condition that allows us to construct an interior proximal method for solving vop on nonpolyhedral set

penalty barrier multiplier methods for convex programming problems we study a class of methods for solving convex programs which are based on nonquadratic augmented lagrangians for which the penalty parameters are functions of the multipliers this gives rise to lagrangians which are nonlinear in the multipliers each augmented lagrangian is specified by a choice of a penalty function varphi and a penalty updating function pi the requirements on varphi are mild and allow for the inclusion of most of the previously suggested augmented lagrangians more importantly a new type of penalty barrier function having a logarithmic branch glued to a quadratic branch is introduced and used to construct an efficient algorithm convergence of the algorithms is proved for the case of pi being a sublinear function of the dual multipliers the algorithms are tested on large scale quadratically constrained problems arising in structural optimization

an analysis of band limited communication systems from amplifier efficiency and distortion perspective considering growing concerns toward green communications not only their bandwidth efficiency but also their power consumption is expected to gain increasing importance for future communication systems a power amplifier pa is one of the most power consuming analog devices at the transmitter in communication systems and a precise estimation of the power consumption at the transmitter circuit requires the knowledge of its efficiency that depends on the distribution of input signal envelope and the amount of input back off in this paper we develop a simple analytical model that can be used for estimating achievable efficiency of a linear pa as well as the amount of resulting nonlinear distortion for a given modulated signal exclusively from its envelope distribution based on this model the trade off relationships between the efficiency and signal to distortion power ratio for several spectrally efficient linear modulations are examined it is also shown that in some special cases of gaussian input and memoryless nonlinearity pa models the results can be represented in simple closed form expressions

lipschitz continuity of solutions of linear inequalities programs and complementarity problems it is shown that solutions of linear inequalities linear programs and certain linear complementarity problems e g those with p matrices or z matrices but not semidefinite matrices are lipschitz continuous with respect to changes in the right hand side data of the problem solutions of linear programs are not lipschitz continuous with respect to the coefficients of the objective function the lipschitz constant given here is a generalization of the role played by the norm of the inverse of a nonsingular matrix in bounding the perturbation of the solution of a system of equations in terms of a right hand side perturbation

separation of nonconvex sets with general augmenting functions in this paper we consider two geometric optimization problems that are dual to each other and characterize conditions under which the optimal values of the two problems are equal this characterization relies on establishing separation results for nonconvex sets using general concave surfaces defined in terms of convex augmenting functions we prove separation results for augmenting functions that are bounded from below unbounded augmenting functions and asymptotic augmenting functions

nonlinear proximal point algorithms using bregman functions with applications to convex programming a bregman function is a strictly convex differentiable function that induces a well behaved distance measure or d function on euclidean space this paper shows that for every bregman function there exists a nonlinear version of the proximal point algorithm and presents an accompanying convergence theory applying this generalization of the proximal point algorithm to convex programming one obtains the d function proximal minimization algorithm of censor and zenios and a wide variety of new multiplier methods these multiplier methods are different from those studied by kort and bertsekas and include nonquadratic variations on the proximal method of multipliers

perturbation analysis of a condition number for convex inequality systems and global error bounds for analytic systems in this paper several types of perturbations on a convex inequality system are considered and conditions are obtained for the system to be well conditioned under these types of perturbations where the well conditionedness of a convex inequality system is defined in terms of the uniform boundedness of condition numbers under a set of perturbations it is shown that certain types of perturbations can be used to characterize the well conditionedness of a convex inequality system in which either the system has a bounded solution set and satisfies the slater condition or an associated convex inequality system which defines the recession cone of the solution set for the system satisfies the slater condition finally sufficient conditions are given for the existence of a global error bound for an analytic system it is shown that such a global error bound always holds for any inequality system defined by finitely many convex analytic functions when the zero vector is in the relative interior of the domain of an associated convex conjugate function

proximal minimization methods with generalized bregman functions we consider methods for minimizing a convex function f that generate a sequence xk by taking xk 1 to be an approximate minimizer of f x dh x xk ck where ck 0 and dh is the d function of a bregman function h extensions are made to b functions that generalize bregman functions and cover more applications convergence is established under criteria amenable to implementation applications are made to nonquadratic multiplier methods for nonlinear programs

modified barrier functions theory and methods the nonlinear rescaling principle employs monotone and sufficiently smooth functions to transform the constraints and or the objective function into an equivalent problem the classical lagrangian which has important properties on the primal and the dual spaces the application of the nonlinear rescaling principle to constrained optimization problems leads to a class of modified barrier functions mbf s and mbf methods mbfm s being classical lagrangians cl s for an equivalent problem the mbf s combine the best properties of the cl s and classical barrier functions cbf s but at the same time are free of their most essential deficiencies due to the excellent mbf properties new characteristics of the dual pair convex programming problems have been found and the duality theory for nonconvex constrained optimization has been developed the mbfm have up to a superlinear rate of convergence and are to the classical barrier functions cbf s method as the multipliers method for augmented lagrangians is to the classical penalty function method based on the dual theory associated with mbf the method for the simultaneous solution of the dual pair convex programming problems with up to quadratic rates of convergence have been developed the application of the mbf to linear lp and quadratic qp programming leads to a new type of multipliers methods which have a much better rate of convergence under lower computational complexity at each step as compared to the cbf methods the numerical realization of the mbfm leads to the newton modified barrier method nmbm the excellent mbf properties allow us to discover that for any nondegenerate constrained optimization problem there exists a hot start from which the nmbm has a better rate of convergence a better complexity bound and is more stable than the interior point methods which are based on the classical barrier functions

interior gradient and epsilon subgradient descent methods for constrained convex minimization we extend epsilon subgradient descent methods for unconstrained nonsmooth convex minimization to constrained problems over polyhedral sets in particular over r p this is done by replacing the usual squared quadratic regularization term used in subgradient schemes by the logarithmic quadratic distancelike function recently introduced by the authors we then obtain interior e subgradient descent methods which allow us to provide a natural extension of bundle methods and polyak s subgradient projection methods for nonsmooth convex minimization furthermore similar extensions are considered for smooth constrained minimization to produce interior gradient descent methods global convergence as well as an improved global efficiency estimate are established for these methods within a unifying principle and minimal assumptions on the problem s data

optimized signal distortion for papr reduction of ofdm signals with ifft fft complexity via admm approaches in this paper we propose two low complexity optimization methods to reduce peak to average power ratio papr values of orthogonal frequency division multiplexing ofdm signals via alternating direction method of multipliers admm first we formulate a nonconvex signal distortion optimization model based on minimizing data carrier distortion such that the constraints are placed on papr and the power of free carriers second to obtain the model s approximate optimal solution efficiently we design two low complexity admm algorithms named admm direct and admm relax respectively third we show that in admm direct relax all the optimization subproblems can be solved semi analytically and the computational complexity in each iteration is roughly mathcal o ell n log 2 ell n where ell and n are over sampling factor and carrier number respectively moreover we show that the resulting solution of admm direct is guaranteed to be some karush kuhn tucker kkt point of the nonconvex model when the iteration algorithm is convergent for admm relax we prove that it has theoretically guaranteed convergence and can approach arbitrarily close to some kkt point of the model if proper parameters are chosen simulation results demonstrate the effectiveness of the proposed approaches

lagrangian duality and related multiplier methods for variational inequality problems we consider a new class of multiplier interior point methods for solving variational inequality problems with maximal monotone operators and explicit convex constraint inequalities developing a simple lagrangian duality scheme which is combined with the recent logarithmic quadratic proximal lqp theory introduced by the authors we derive three algorithms for solving the variational inequality vi problem this provides a natural extension of the methods of multipliers used in convex optimization and leads to smooth interior point multiplier algorithms we prove primal dual and primal dual convergence under very mild assumptions eliminating all the usual assumptions used until now in the literature for related algorithms applications to complementarity problems are also discussed

convergence of proximal like algorithms we analyze proximal methods based on entropy like distances for the minimization of convex functions subject to nonnegativity constraints we prove global convergence results for the methods with approximate minimization steps and an ergodic convergence result for the case of finding a zero of a maximal monotone operator we also consider linearly constrained convex problems and establish a quadratic convergence rate result for linear programs our analysis allows us to simplify and extend the available convergence results for these methods

a practical general approximation criterion for methods of multipliers based on bregman distances this paper demonstrates that for generalized methods of multipliers for convex programming based on bregman distance kernels including the classical quadratic method of multipliers the minimization of the augmented lagrangian can be truncated using a simple generally implementable stopping criterion based only on the norms of the primal iterate and the gradient or a subgradient of the augmented lagrangian at that iterate previous results in this and related areas have required conditions that are much harder to verify such as e optimality with respect to the augmented lagrangian or strong conditions on the convex program to be solved here only existence of a kkt pair is required and the convergence properties of the exact form of the method are preserved the key new element in the analysis is the use of a full conjugate duality framework as opposed to mainly examining the action of the method on the standard dual function of the convex program an existence result for the iterates stronger than those possible for the exact form of the algorithm is also included

lagrangian regularization approach to constrained optimization problems abstract this paper proposes a new regularization approach referred to as the lagrangian regularization approach which aims to circumvent the nondifferentiability of a positively homogeneous function r m in a conceptual unconstrained reformulation for constrained optimization problems with the appropriate choices of regularizing function we obtain a family of smooth functions that include as special cases the existing penalty and barrier functions as such our approach can be used as an instrumental tool to resolve the nondifferentiability of r m as well as a unified way to construct penalty functions for convex programming cases we present its global convergence analysis

augmented lagrangian applied to convex quadratic problems an algorithm based on the augmented lagrangian method is proposed to solve convex quadratic programming problem the quadratic penalty is considered here hence the augmented lagrangian function is quadratic when applied to quadratic programming problem for this penalty we show that if the lagrangian function associated with the original problem is strict convex or convex then the hessian matrix of augmented lagrangian function is positive definite or positive semi definite numerical experiments are presented illustrating the performance of the algorithm for the cute test set

performance analysis of deliberately clipped ofdm signals we analyze the performance of the clipped orthogonal frequency division multiplexing ofdm system in terms of peak power reduction capability and degradation of channel capacity the clipping is performed on the baseband ofdm signals with and without oversampling followed by the ideal low pass filter first the effect of the envelope clipping on the peak to average power ratio papr and the instantaneous power of the band limited ofdm signal is studied we then discuss the channel capacity of the oversampled and clipped ofdm signals over the additive white gaussian noise and ideally interleaved rayleigh fading channels the capacity is calculated based on the assumption that the distortion terms caused by the clipping are gaussian it is shown that the snr penalty due to the clipping can be considerably alleviated by using optimal coding and reducing the information data rate the results are justified by the simulation results using near optimal turbo codes

the semi explicit volterra integral algebraic equations with weakly singular kernels the numerical treatments this paper deals with some theoretical and numerical results for volterra integral algebraic equations iaes of index 1 with weakly singular kernels this type of equations typically has solutions whose derivatives are unbounded at the left endpoint of the interval of integration for overcoming this non smooth behavior of solutions using the appropriate coordinate transformation the primary system is changed into a new iaes which its solutions have better regularity an effective numerical method based on the chebyshev collocation scheme is designed and its convergence analysis is provided our numerical experiments show that the theoretical results are in good accordance with actual convergence rates obtained by the given algorithm

entropic proximal decomposition methods for convex programs and variational inequalities we consider convex optimization and variational inequality problems with a given separable structure we propose a new decomposition method for these problems which combines the recent logarithmic quadratic proximal theory introduced by the authors with a decomposition method given by chen teboulle for convex problems with particular structure the resulting method allows to produce for the first time provably convergent decomposition schemes based on c lagrangians for solving convex structured problems under the only assumption that the primal dual problems have nonempty solution sets global convergence of the primal dual sequences produced by the algorithm is established

performance analysis for ofdm signals with peak cancellation peak cancellation pc is known as one of the simplest peak to average power ratio papr reduction techniques that are applicable to various communications standards the salient advantage of pc is its ease of hardware implementation but it induces in band distortion and out of band radiation in order to restrict the amount of distortion within an acceptable level it is critical to carefully design the cancelling pulses as well as the envelope threshold over which pc is applied in most studies however they are determined empirically through computer simulations this paper thus focuses on a rigorous theoretical analysis of pc applied to band limited orthogonal frequency division multiplexing ofdm signals and discusses its validity and limitation for practical applications based on the level crossing rate approximation of the peak distribution we derive a closed form expression for the achievable signal to distortion power ratio sdr we also analyze the adjacent channel leakage ratio aclr as well as error vector magnitude evm with which the symbol error rate ser over an additive white gaussian noise awgn channel is obtained all the theoretical results developed in this work are compared with those based on the corresponding computer simulations to justify our analytical approach it thus serves as a useful and accurate tool for designing cancelling pulses as well as the threshold level for given specific system requirements such as sdr or evm and aclr

barrier operators and associated gradient like dynamical systems for constrained minimization problems we study some continuous dynamical systems associated with constrained optimization problems for that purpose we introduce the concept of elliptic barrier operators and develop a unified framework to derive and analyze the associated class of gradient like dynamical systems called a driven descent method a dm prominent methods belonging to this class include several continuous descent methods studied earlier in the literature such as steepest descent method continuous gradient projection methods and newton type methods as well as continuous interior descent methods such as lotka volterra type differential equations and riemannian gradient methods related discrete iterative methods such as proximal interior point algorithms based on bregman functions and second order homogeneous kernels can also be recovered within our framework and allow for deriving some new and interesting dynamics we prove global existence and strong viability results of the corresponding trajectories of a dm for a smooth objective function when the objective function is convex we analyze the asymptotic behavior at infinity of the trajectory produced by the proposed class of dynamical systems a dm in particular we derive a general criterion ensuring the global convergence of the trajectory of a dm to a minimizer of a convex function over a closed convex set this result is then applied to several dynamics built upon specific elliptic barrier operators throughout the paper our results are illustrated with many examples

an analysis of the em algorithm and entropy like proximal point methods the em algorithm is a popular method for maximum likelihood estimation from incomplete data this method may be viewed as a proximal point method for maximizing the log likelihood function using an integral form of the kullback leibler distance function motivated by this interpretation we consider a proximal point method using an integral form of entropy like distance function we give a convergence analysis of the resulting proximal point method in the case where the cluster points lie in the interior of the objective function domain this result is applied to a normal independent example and a gaussian mixture example to establish convergence of the em algorithm on these examples further convergence analysis of the method for maximization over an orthant is given in low dimensions sublinear convergence and schemes for accelerating convergence are also discussed

multiplicative iterative algorithms for convex programming abstract we study multiplicative iterative algorithms for the minimization of a differentiable convex function defined on the positive orthant of r n if the objective function has compact level sets and has a locally lipschitz continuous gradient then these algorithms converge to a solution of the minimization problem moreover the convergence is nearly monotone in the sense of kullback leibler divergence special cases of these algorithms have been applied in position emission tomography and are formally related to the em algorithm for position emission tomography

a hybrid entropic proximal decomposition method with self adaptive strategy for solving variational inequality problems in this paper we propose a hybrid nonlinear decomposition projection method for solving a class of monotone variational inequality problems the algorithm utilizes the problems structure conductive to decomposition and a projection step to get the next iterate to make the method more practical we allow solving of the subproblems approximately and adopt the constructive accuracy criterion developed recently by solodov and svaiter for classical proximal point algorithm and by the author for generalized proximal point algorithm the fejer monotonicity to the solution set of the problem is obtained by only assuming the underlying mapping is monotone and the solution set is nonempty the parameter is allowed to vary in a larger interval than that of auslender and teboulle and we also propose some improved self adaptive strategies to choose the sequence of parameters which makes the algorithm more flexible

nonlinear rescaling vs smoothing technique in convex optimization we introduce an alternative to the smoothing technique approach for constrained optimization as it turns out for any given smoothing function there exists a modification with particular properties we use the modification for nonlinear rescaling nr the constraints of a given constrained optimization problem into an equivalent set of constraints the constraints transformation is scaled by a vector of positive parameters the lagrangian for the equivalent problems is to the correspondent smoothing penalty functions as augmented lagrangian to the classical penalty function or mbfs to the barrier functions moreover the lagrangians for the equivalent problems combine the best properties of quadratic and nonquadratic augmented lagrangians and at the same time are free from their main drawbacks sequential unconstrained minimization of the lagrangian for the equivalent problem in primal space followed by both lagrange multipliers and scaling parameters update leads to a new class of nr multipliers methods which are equivalent to the interior quadratic prox methods for the dual problem we proved convergence and estimate the rate of convergence of the nr multipliers method under very mild assumptions on the input data we also estimate the rate of convergence under various assumptions on the input data in particular under the standard second order optimality conditions the nr method converges with q linear rate without unbounded increase of the scaling parameters which correspond to the active constraints we also established global quadratic convergence of the nr methods for linear programming with unique dual solution we provide numerical results which strongly support the theory

a simplified view of first order methods for optimization we discuss the foundational role of the proximal framework in the development and analysis of some iconic first order optimization algorithms with a focus on non euclidean proximal distances of bregman type which are central to the analysis of many other fundamental first order minimization relatives we stress simplification and unification by highlighting self contained elementary proof patterns to obtain convergence rate and global convergence both in the convex and the nonconvex settings which in turn also allows to present some novel results

the numerical solution of integral algebraic equations of index 1 by polynomial spline collocation methods in this paper we study polynomial spline collocation methods applied to a particular class of integral algebraic equations of volterra type we analyse mixed systems of second and first kind integral equations global convergence and local superconvergence results are established

convergence rate analysis of nonquadratic proximal methods for convex and linear programming the divergence proximal method is an extension of the proximal minimization algorithm where the usual quadratic proximal term is substituted by a class of convex statistical distances called divergences in this paper we study the convergence rate of this nonquadratic proximal method for convex and particularly linear programming we identify a class of divergences for which superlinear convergence is attained both for optimization problems with strongly convex objectives at the optimum and linear programming problems when the regularization parameters tend to zero we prove also that with regularization parameters bounded away from zero convergence is at least linear for a wider class of divergences when the method is applied to the same kinds of problems we further analyze the associated class of augmented lagrangian methods for convex programming with nonquadratic penalty terms and prove convergence of the dual generated by these methods for linear programming problems under a weak nondegeneracy assumption

convergence analysis of a proximal like minimization algorithm using bregman functions an alternative convergence proof of a proximal like minimization algorithm using bregman functions recently proposed by censor and zenios is presented the analysis allows the establishment of a global convergence rate of the algorithm expressed in terms of function values

an interior proximal algorithm and the exponential multiplier method for semidefinite programming we introduce an interior proximal algorithm for semidefinite optimization problems and establish its convergence properties we also study the corresponding dual algorithm leading to an exponential multiplier method for semidefinite programs potential applications and extensions are also discussed

a theoretical characterization of nonlinear distortion effects in ofdm systems this paper presents a theoretical characterization of nonlinear distortion effects in orthogonal frequency division multiplexing ofdm transmission systems in the theoretical framework developed it is shown that the effects on the decision variables of the in band distortion introduced by a bandpass memoryless nonlinearity can be described by means of a complex gain and an additive gaussian term with zero mean and suitable variance analytical expressions for gain and variance are given the conditions which allow this description are emphasized and discussed as a consequence a completely analytical procedure to evaluate error probability is also obtained and illustrated using ofdm discrete multitone modulation dmt systems with rectangular pulse shaping for the soft envelope limiter nonlinearity a closed form is derived a comparison with simulation results is carried out to verify the accuracy of this method

a generalization of the proximal point algorithm the problem considered in this paper is to find a solution to the generalized equation 0 in t x y where t is a maximal monotone operator on the product h 1 times h 2 of two hilbert spaces h 1 and h 2 we give a generalization of the proximal map and the proximal point algorithm in which the proposed iterative procedure is based on just one variable applying to convex programming problems instead of adding a quadratic term for all variables as in the proximal point algorithm a quadratic term for a subset of variables is added this paper proves that under a mild assumption our algorithm has the same convergence properties as the regular proximal point algorithm

inexact proximal point methods for variational inequality problems we present a new family of proximal point methods for solving monotone variational inequalities our algorithm has a relative error tolerance criterion in solving the proximal subproblems our convergence analysis covers a wide family of regularization functions including double regularizations recently introduced by silva eckstein and humes jr siam j optim 12 2001 pp 238 261 and the bregman distance induced by h x sum i 1 n x i log x i we do not use in our analysis the assumption of paramonotonicity which is standard in proving convergence of bregman based proximal methods

building initial partitions through sampling techniques a variety of iterative clustering algorithms require an initial partition of a dataset as an input parameter as a rule a good choice of the initial partition is essential for building a high quality final partition in this note we generate initial partitions by using small samples of the data numerical experiments with k means like clustering algorithms are reported

an extension of proximal methods for quasiconvex minimization on the nonnegative orthant abstract in this paper we propose an extension of proximal methods to solve minimization problems with quasiconvex objective functions on the nonnegative orthant assuming that the function is bounded from below and lower semicontinuous and using a general proximal distance it is proved that the iterations given by our algorithm are well defined and stay in the positive orthant if the objective function is quasiconvex we obtain the convergence of the iterates to a certain set which contains the set of optimal solutions and convergence to a kkt point if the function is continuously differentiable and the proximal parameters are bounded furthermore we introduce a sufficient condition on the proximal distance such that the sequence converges to an optimal solution of the problem

differential algebraic equations indices and integral algebraic equations in a recent report hairer lubich and roche report ch 1211 dept de mathematiques universite de geneve geneve switzerland 1988 define the index of differential algebraic equations daes by considering the effect of perturbations of the equations on the solutions this index which will be called the perturbation index p i is one more than the number of derivatives of the perturbation that must appear in any estimate of the bound of the change in the solution an earlier form of index used by a number of authors including gear and petzold siam j numer anal 21 1984 pp 716 728 is determined by the number of differentiations of the daes that are required to generate an ordinary differential equation ode satisfied by the solution this will be called the differential index d i hairer lubich and roche give an example whose differential index is one and perturbation index is two and other examples where they are identical it will be shown that d i leqq p i leqq d i 1 and th

optimal convergence results of piecewise polynomial collocation solutions for integral algebraic equations of index 3 in this work we will consider piecewise polynomial collocation methods for a new class of integral algebraic equations of index 3 an analysis of the global convergence properties of the collocation methods is given and the optimal order of convergence results is established the performance of the proposed scheme is illustrated by means of two numerical examples and confirm that we can achieve the expected theoretical orders of convergence

interior proximal and multiplier methods based on second order homogeneous kernels we study a class of interior proximal algorithms and nonquadratic multiplier methods for solving convex programs where the usual proximal quadratic term is replaced by an homogeneous functional of order two defined in terms of a convex function we prove under mild assumptions several new convergence results in both the primal and dual framework allowing also for approximate minimization in particular we introduce a new class of interior proximal methods which is globally convergent and allows for generating c multiplier methods with bounded hessians which exhibit strong convergence properties we also consider linearly constrained convex problems and establish global quadratic convergence rates results for linear programs we then study in detail a particular realization of these algorithms leading to a new class of logarithmic quadratic interior point algorithms which are shown to enjoy several attractive properties for solving constrained convex optimization problems

nonlinear rescaling and proximal like methods in convex optimization the nonlinear rescaling principle nrp consists of transforming the objective function and or the constraints of a given constrained optimization problem into another problem which is equivalent to the original one in the sense that their optimal set of solutions coincides a nonlinear transformation parameterized by a positive scalar parameter and based on a smooth sealing function is used to transform the constraints the methods based on nrp consist of sequential unconstrained minimization of the classical lagrangian for the equivalent problem followed by an explicit formula updating the lagrange multipliers we first show that the nrp leads naturally to proximal methods with an entropy like kernel which is defined by the conjugate of the scaling function and establish that the two methods are dually equivalent for convex constrained minimization problems we then study the convergence properties of the nonlinear rescaling algorithm and the corresponding entropy like proximal methods for convex constrained optimization problems special cases of the nonlinear rescaling algorithm are presented in particular a new class of exponential penalty modified barrier functions methods is introduced

rescaling and stepsize selection in proximal methods using separable generalized distances this paper presents a convergence proof technique for a broad class of proximal algorithms in which the perturbation term is separable and may contain barriers enforcing interval constraints there are two key ingredients in the analysis a mild regularity condition on the differential behavior of the barrier as one approaches an interval boundary and a lower stepsize limit that takes into account the curvature of the proximal term we give two applications of our approach first we prove subsequential convergence of a very broad class of proximal minimization algorithms for convex optimization where different stepsizes can be used for each coordinate applying these methods to the dual of a convex program we obtain a wide class of multiplier methods with subsequential convergence of both primal and dual iterates and independent adjustment of the penalty parameter for each constraint the adjustment rules for the penalty parameters generalize a well established scheme for the exponential method of multipliers the results may also be viewed as a generalization of recent work by ben tal and zibulevsky siam j optim 7 1997 pp 347 366 and auslender teboulle and ben tiba comput optim appl 12 1999 pp 31 40 math oper res 24 1999 pp 645 668 on methods derived from varphi divergences the second application established full convergence under a novel stepsize condition of bregman function based proximal methods for general monotone operator problems over a box prior results in this area required strong restrictive assumptions on the monotone operator

integral algebraic equations theory of collocation methods i our analysis of collocation solutions for general systems of linear integral algebraic equations iaes is based on the notions of the tractability index and the nu smoothing property of a volterra integral operator these are used to decouple the given iae system into the inherent system of regular second kind volterra integral equations vies and a system of first kind vies this decoupling is then used to derive the optimal convergence properties of piecewise polynomial collocation solutions numerical examples illustrate the theoretical results

asymptotic analysis for penalty and barrier methods in convex and linear programming we consider a wide class of penalty and barrier methods for convex programming which includes a number of specific functions proposed in the literature we provide a systematic way to generate penalty and barrier functions in this class and we analyze the existence of primal and dual optimal paths generated by these penalty methods as well as their convergence to the primal and dual optimal sets for linear programming we prove that these optimal paths converge to single points

message passing for graph structured linear programs proximal methods and rounding schemes the problem of computing a maximum a posteriori map configuration is a central computational challenge associated with markov random fields there has been some focus on tree based linear programming lp relaxations for the map problem this paper develops a family of super linearly convergent algorithms for solving these lps based on proximal minimization schemes using bregman divergences as with standard message passing on graphs the algorithms are distributed and exploit the underlying graphical structure and so scale well to large problems our algorithms have a double loop character with the outer loop corresponding to the proximal sequence and an inner loop of cyclic bregman projections used to compute each proximal update we establish convergence guarantees for our algorithms and illustrate their performance via some simulations we also develop two classes of rounding schemes deterministic and randomized for obtaining integral configurations from the lp solutions our deterministic rounding schemes use a re parameterization property of our algorithms so that when the lp solution is integral the map solution can be obtained even before the lp solver converges to the optimum we also propose graph structured randomized rounding schemes applicable to iterative lp solving algorithms in general we analyze the performance of and report simulations comparing these rounding schemes

a class of nonlinear signal processing schemes for bandwidth efficient ofdm transmission with low envelope fluctuation this work presents a wide class of digital signal processing schemes for orthogonal frequency division multiplexing ofdm transmission which combine a nonlinear operation in the time domain and a linear filtering operation in the frequency domain the ultimate goal of these schemes is to reduce the envelope fluctuation of ordinary ofdm while keeping its high spectral efficiency and allowing a low cost power efficient implementation an appropriate statistical model concerning the transmitted frequency domain blocks is developed which is derived from well established results on gaussian stochastic processes distorted by memoryless nonlinearities this model can be employed for performance evaluation by analytical means with highly accurate results whenever the corresponding conventional ofdm signals exhibit quasi gaussian characteristics cases where the signal processing scheme is repeatedly used in an iterative way are treated through an extension of the proposed statistical modeling a set of numerical results is presented and discussed so as to show the practical interest of both the proposed schemes and the analytical methods for evaluation of their performance for the sake of comparisons this paper includes numerical results concerning the partial transmit sequence technique which is an alternative peak to mean envelope power ratio reducing technique of higher complexity often recommended due to its distortionless nature the superior performance complexity tradeoffs through the proposed class of nonlinear signal processing schemes is emphasized

structural analysis of linear integral algebraic equations abstract the choice of a feasible numerical method for the solution of an integral algebraic equation iae requires knowledge about its index and solvability in this paper the method for structural analysis of differential algebraic equation systems daes is extended to analyze the structure of a linear iae its index and solvability are determined based on the sparsity pattern of the iae and the smoothing property of a volterra integral operator

an inexact proximal method for quasiconvex minimization abstract in this paper we propose an inexact proximal point method to solve constrained minimization problems with locally lipschitz quasiconvex objective functions assuming that the function is also bounded from below lower semicontinuous and using proximal distances we show that the sequence generated for the method converges to a stationary point of the problem

interior projection like methods for monotone variational inequalities we propose new interior projection type methods for solving monotone variational inequalities the methods can be viewed as a natural extension of the extragradient and hyperplane projection algorithms and are based on using non euclidean projection like maps we prove global convergence results and establish rate of convergence estimates the projection like maps are given by analytical formulas for standard constraints such as box simplex and conic type constraints and generate interior trajectories we then demonstrate that within an appropriate primal dual variational inequality framework the proposed algorithms can be applied to general convex constraints resulting in methods which at each iteration entail only explicit formulas and do not require the solution of any convex optimization problem as a consequence the algorithms are easy to implement with low computational cost and naturally lead to decomposition schemes for problems with a separable structure this is illustrated through examples for convex programming convex concave saddle point problems and semidefinite programming

on the convergence of the exponential multiplier method for convex programming in this paper we analyze the exponential method of multipliers for convex constrained minimization problems which operates like the usual augmented lagrangian method except that it uses an exponential penalty function in place of the usual quadratic we also analyze a dual counterpart the entropy minimization algorithm which operates like the proximal minimization algorithm except that it uses a logarithmic entropy proximal term in place of a quadratic we strengthen substantially the available convergence results for these methods and we derive the convergence rate of these methods when applied to linear programs

differential algebraic equations of index 1 may have an arbitrarily high structural index it is shown that the structural index of a linear differential algebraic equation dae with constant coefficients and with index 1 may be arbitrarily high contrary to a previous result from the literature this demonstrates that pantelides algorithm applied to daes of index 1 may perform an arbitrarily high number of iterations and differentiations

entropic proximal mappings with applications to nonlinear programming we introduce a family of new transforms based on imitating the proximal mapping of moreau and the associated moreau yosida proximal approximation of a function the transforms are constructed in terms of the a divergence functional a generalization of the relative entropy and of bregman s measure of distance an analogue of moreau s theorem associated with these entropy like distances is proved we show that the resulting entropic proximal maps share properties similar to the proximal mapping and provide a fairly general framework for constructing approximation and smoothing schemes for optimization problems applications of the results to the construction of generalized augmented lagrangians for nonlinear programs and the minimax problem are presented