an inexact augmented lagrangian multiplier method for solving quadratic complementary problems an adapted algorithmic framework combining specific resolution techniques abstract in this paper an inexact augmented lagrangian multiplier method alm is designed for solving the quadratic complementarity problem qcp the primary goal is proposing an algorithm exploring the structures of qcps and incorporating them into the implementation in the implementation an inexact proximal alternating minimization method is employed to solve the augmented lagrangian subproblems as a result all the subproblems are either strongly convex quadratic programs or linear equations with positive semidefinite symmetric coefficient matrices which in turn can either be solved with explicitly formula solutions or by an accelerated proximal gradient method or a conjugate gradient method convergence rates of these subproblems are given and global convergence of the alm algorithm is established under mild assumptions preliminary numerical experiments show that the algorithm is feasible and efficient

the approximation of separable stochastic programs abstract stochastic programming sp problems with separable cost functions are considered special attention being paid to simple and linear quadratic recourse using barycentric approximation schemes and their features we derive convergent sub sequences of approximate solutions and of associated error bounds for the given problem based on structural properties that until now have not been exploited a further contribution of the present paper is seen in the convergence statements yielding argmin convergence assuming the sets of global minimizers of the approximate functions are nonempty argmin convergence is obtained by restricting the conditions of epi convergence to the sets of minimizers that correspond to the approximate functions

mean field stochastic theory for species rich assembled communities a dynamical model of an ecological community is analyzed within a mean field approximation in which one of the species interacts with the combination of all of the other species in the community within this approximation the model may be formulated as a master equation describing a one step stochastic process the stationary distribution is obtained in closed form and is shown to reduce to a log series or log normal distribution depending on the values that the parameters describing the model take on a hyperbolic relationship between the connectance of the matrix of interspecies interactions and the average number of species exists for a range of parameter values the time evolution of the model at short and intermediate times is analyzed using van kampen s approximation which is valid when the number of individuals in the community is large good agreement with numerical simulations is found the large time behavior and the approach to the stationary state is obtained by solving the equation for the generating function of the probability distribution the analytical results which follow from the analysis are also in good agreement with direct simulations of the model

a relaxed constant positive linear dependence constraint qualification and applications in this work we introduce a relaxed version of the constant positive linear dependence constraint qualification cpld that we call rcpld this development is inspired by a recent generalization of the constant rank constraint qualification by minchenko and stakhovski that was called rcrcq we show that rcpld is enough to ensure the convergence of an augmented lagrangian algorithm and that it asserts the validity of an error bound we also provide proofs and counter examples that show the relations of rcrcq and rcpld with other known constraint qualifications in particular rcpld is strictly weaker than cpld and rcrcq while still stronger than abadie s constraint qualification we also verify that the second order necessary optimality condition holds under rcrcq

a note on an approximate lagrange multiplier rule in this note we show that for a large class of optimization problems the lagrange multiplier rule can be derived from the approximate multiplier rule

second order optimality conditions in nonlinear programming obtained by way of epi derivatives dedicated to the memory of robin w chaney second order optimality conditions for finite dimensional smooth and nonsmooth nonlinear programming are obtained by a new method that emphasizes a close connection with geometrical approximation of the essential objective function the approximation is secured by the use of certain epi derivatives defined by epiconvergence the optimality conditions are expressed in a form that covers general interval constraints and their possible representation through penalties or an augmented lagrangian an abstract constraint involving restriction to a convex polyhedron is incorporated

control volume approximation of degenerate two phase porous flows implicit euler approximations of the equations governing the porous flow of two immiscible incompressible fluids are shown to be the euler lagrange equations of a convex function tools from conve

two new weak constraint qualifications and applications we present two new constraint qualifications cqs that are weaker than the recently introduced relaxed constant positive linear dependence rcpld cq rcpld is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally a major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a cq this is done in the first new cq which we call the constant rank of the subspace component crsc cq this new cq also preserves many of the good properties of rcpld such as local stability and the validity of an error bound we also introduce an even weaker cq called the constant positive generator cpg which can replace rcpld in the analysis of the global convergence of algorithms we close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods sequential quadratic programming augmented lagrangians

optimality conditions for non finite valued convex composite functions burke 1987 has recently developed second order necessary and sufficient conditions for convex composite optimization in the case where the convex function is finite valued in this note we present a technique for reducing the infinite valued case to the finite valued one we then use this technique to extend the results in burke 1987 to the case in which the convex function may take infinite values we conclude by comparing these results with those established by rockafellar 1989 for the piecewise linear quadratic case

finitely connected vector spin systems with random matrix interactions we use finite connectivity equilibrium replica theory to solve models of finitely connected unit length vectorial spins with random pair interactions which are of the orthogonal matrix type finitely connected spin models although still of a mean field nature can be regarded as a convenient level of description in between fully connected and finite dimensional ones since the spins are continuous and the connectivity c remains finite in the thermodynamic limit the replica symmetric order parameter is a functional the general theory is developed for arbitrary values of the dimension d of the spins and arbitrary choices of the ensemble of random orthogonal matrices we calculate phase diagrams and the values of moments of the order parameter explicitly for d 2 finitely connected xy spins with random chiral interactions and for d 3 finitely connected classical heisenberg spins with random chiral interactions numerical simulations are shown to support our predictions quite satisfactorily

an augmented lagrangian approach with a variable transformation in nonlinear programming abstract tangent cone and regular normal cone of a closed set under an invertible variable transformation around a given point are investigated which lead to the concepts of 1 tangent cone of a set and 1 subderivative of a function when the notion of 1 subderivative is applied to perturbation functions a class of augmented lagrangians involving an invertible mapping of perturbation variables are obtained in which dualizing parameterization and augmenting functions are not necessarily convex in perturbation variables a necessary and sufficient condition for the exact penalty representation under the proposed augmented lagrangian scheme is obtained for an augmenting function with an euclidean norm a sufficient condition resp a sufficient and necessary condition for an arbitrary vector resp 0 to support an exact penalty representation is given in terms of 1 subderivatives an example of the variable transformation applied to constrained optimization problems is given which yields several exact penalization results in the literature

identification of nth power velocity damping this paper demonstrates how the two damping parameters associated with the non linear nth power velocity model can be identified from the time series records of the displacement and velocity responses to sinusoidal excitation no restriction is imposed on the level of damping present and estimates are acquired by minimizing the square of the error between observed responses and those predicted by a linearized model the problems of noise contamination and uncertain initial conditions are treated by using simulated data and converged estimates are presented with computation times measured in cpu seconds on a vax 11780 computer

power law damping parameter identification abstract the parameter estimation of a nonlinear power damping system is studied the parameter identification method used here assumes a priori the equation of motion describing the system dynamics the method which is based on the measured data acceleration was applied to the free and forced vibrations the identification procedure was found to be robust on the guessed value of parameters at the numerical experimentation the parameter values were estimated with a good accuracy for both modes of system operation free and forced if only the measured time history was sampled at a high enough rate for the noise level contained within it was shown that the steady state of the harmonically excited system is not the best region for the parameter identification with this method during the experimentation the method was applied to the free vibrations in different media air and water the results obtained by the parameter identification method were compared to the ones obtained by separate tests and good agreement was found the identification procedure was found to work fine for all models under consideration and the models responses correspond well to the measured acceleration time histories

predator prey cycles from resonant amplification of demographic stochasticity we present the simplest individual level model of predator prey dynamics and show via direct calculation that it exhibits cycling behavior the deterministic analogue of our model recovered when the number of individuals is infinitely large is the volterra system with density dependent prey reproduction which is well known to fail to predict cycles this difference in behavior can be traced to a resonant amplification of demographic fluctuations which disappears only when the number of individuals is strictly infinite our results indicate that additional biological mechanisms such as predator satiation may not be necessary to explain observed predator prey cycles in real finite populations

variational properties of value functions regularization plays a key role in a variety of optimization formulations of inverse problems a recurring theme in regularization approaches is the selection of regularization parameters and their effect on the solution and on the optimal value of the optimization problem the sensitivity of the value function to the regularization parameter can be linked directly to the lagrange multipliers this paper characterizes the variational properties of the value functions for a broad class of convex formulations which are not all covered by standard lagrange multiplier theory an inverse function theorem is given that links the value functions of different regularization formulations not necessarily convex these results have implications for the selection of regularization parameters and the development of specialized algorithms numerical examples illustrate the theoretical results

augmented lagrangian methods under the constant positive linear dependence constraint qualification two augmented lagrangian algorithms for solving kkt systems are introduced the algorithms differ in the way in which penalty parameters are updated possibly infeasible accumulation points are characterized it is proved that feasible limit points that satisfy the constant positive linear dependence constraint qualification are kkt solutions boundedness of the penalty parameters is proved under suitable assumptions numerical experiments are presented

knapsack problems with sigmoid utilities approximation algorithms via hybrid optimization we study a class of non convex optimization problems involving sigmoid functions we show that sigmoid functions impart a combinatorial element to the optimization variables and make the global optimization computationally hard we formulate versions of the knapsack problem the generalized assignment problem and the bin packing problem with sigmoid utilities we merge approximation algorithms from discrete optimization with algorithms from continuous optimization to develop approximation algorithms for these np hard problems with sigmoid utilities

local convergence of exact and inexact augmented lagrangian methods under the second order sufficient optimality condition we establish local convergence and rate of convergence of the classical augmented lagrangian algorithm under the sole assumption that the dual starting point is close to a multiplier satisfying the second order sufficient optimality condition in particular no constraint qualifications of any kind are needed previous literature on the subject required in addition the linear independence constraint qualification and either the strict complementarity assumption or a stronger version of the second order sufficient condition that said the classical results allow the initial multiplier estimate to be far from the optimal one at the expense of proportionally increasing the threshold value for the penalty parameters although our primary goal is to avoid constraint qualifications if the stronger assumptions are introduced then starting points far from the optimal multiplier are allowed within our analysis as well using only the second order sufficient optimality condition for penalty parameters large

brief paper robust pid controller tuning based on the heuristic kalman algorithm this paper presents a simple but effective tuning strategy for robust pid controllers satisfying multiple h performance criteria finding such a controller is known to be computationally intractable via the conventional techniques this is mainly due to the non convexity of the resulting control problem which is of the fixed order structure type to solve this kind of control problem easily and directly without using any complicated mathematical manipulations and without using too many user defined parameters we utilize the heuristic kalman algorithm hka for the resolution of the underlying constrained non convex optimization problem the resulting tuning strategy is applicable both to stable and unstable systems without any limitation concerning the order of the process to be controlled various numerical studies are conducted to demonstrate the validity of the proposed tuning procedure comparisons with previously published works are also given

differential systems for constrained optimization via a nonlinear augmented lagrangian abstract a general differential system framework for solving constrained optimization problems is investigated which relies on a class of nonlinear augmented lagrangians the differential systems mainly consist of first order derivatives and second order derivatives of the nonlinear augmented lagrangian under suitable conditions the asymptotic stability of the differential systems and local convergence properties of their euler discrete schemes are obtained including the locally quadratic convergence rate of the discrete sequence for the second order derivatives based differential system furthermore as the special case the exponential lagrangian applied to this framework is given numerical experiments are presented illustrating the performance of the differential systems

on convexity of error rates in digital communications convexity properties of error rates of a class of decoders including the maximum likelihood min distance one as a special case are studied for arbitrary constellations bit mapping and coding earlier results obtained for the additive white gaussian noise channel are extended to a wide class of noise densities including unimodal and spherically invariant noise under these broad conditions symbol and bit error rates are shown to be convex functions of the signal to noise ratio snr in the high snr regime with an explicitly determined threshold which depends only on the constellation dimensionality and minimum distance thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way it is the decreasing nature of the noise power density around the decision region boundaries that ensures the convexity of symbol error rates in the general case the known high low snr bounds of the convexity concavity regions are tightened and no further improvement is shown to be possible in general the high snr bound fits closely into the channel coding theorem all codes including capacity achieving ones whose decision regions include the hardened noise spheres from the noise sphere hardening argument in the channel coding theorem satisfy this high snr requirement and thus has convex error rates in both snr and noise power we conjecture that all capacity achieving codes have convex error rates convexity properties in signal amplitude and noise power are also investigated some applications of the results are discussed in particular it is shown that fading is convexity preserving and is never good in low dimensions under spherically invariant noise which may also include any linear diversity combining

enhanced fritz john conditions for convex programming we consider convex constrained optimization problems and we enhance the classical fritz john optimality conditions to assert the existence of multipliers with special sensitivity properties in particular we prove the existence of fritz john multipliers that are informative in the sense that they identify constraints whose relaxation at rates proportional to the multipliers strictly improves the primal optimal value moreover we show that if the set of geometric multipliers is nonempty then the minimum norm vector of this set is informative and defines the optimal rate of cost improvement per unit constraint violation our assumptions are very general and in particular allow for the presence of a duality gap and the nonexistence of optimal solutions in particular for the case where there is a duality gap we establish enhanced fritz john conditions involving the dual optimal value and dual optimal solutions

parameter estimation for hysteretic systems abstract the differential system characterization of hysteretic system is well known the problem of estimating the parameters of this system on the basis of input output data possibly noise corrupted is considered it turns out that the estimation problem is a non linear optimization problem the gauss newton method is used in setting up a two stage iterative least squares algorithm the usefulness of the algorithm is validated through its application to various simulated time histories from the hysteretic model

penalty function methods and a duality gap for invex optimization problems abstract in this paper the penalty function method is used to study duality in nonconvex mathematical programming problems in particular we prove the zero duality gap between optimization problems involving invex functions with respect to the same function and their lagrangian dual problems the results proved in the paper are illustrated by suitable examples of nonconvex optimization problems

a cone continuity constraint qualification and algorithmic consequences every local minimizer of a smooth constrained optimization problem satisfies the sequential approximate karush kuhn tucker akkt condition this optimality condition is used to define the stopping criteria of many practical nonlinear programming algorithms it is natural to ask for conditions on the constraints under which akkt implies kkt these conditions will be called strict constraint qualifications scqs in this paper we define a cone continuity property ccp that will be shown to be the weakest possible scq its relation to other constraint qualifications will also be clarified in particular it will be proved that ccp is strictly weaker than the constant positive generator constraint qualification

ecological communities with lotka volterra dynamics ecological communities in heterogeneous environments assemble through the combined effect of species interaction and migration understanding the effect of these processes on the community properties is central to ecology here we study these processes for a single community subject to migration from a pool of species with population dynamics described by the generalized lotka volterra equations we derive exact results for the phase diagram describing the dynamical behaviors and for the diversity and species abundance distributions a phase transition is found from a phase where a unique globally attractive fixed point exists to a phase where multiple dynamical attractors exist leading to history dependent community properties the model is shown to possess a symmetry that also establishes a connection with other well known models

approximating subdifferentials by random sampling of gradients many interesting real functions on euclidean space are differentiable almost everywhere all lipschitz functions have this property but so for example does the spectral abscissa of a matrix a non lipschitz function in practice the gradient is often easy to compute we investigate to what extent we can approximate the clarke subdifferential of such a function at some point by calculating the convex hull of some gradients sampled at random nearby points

a decrement method for quantifying nonlinear and linear damping parameters a method is presented which can estimate the linear and nonlinear damping parameters in a lightly damped system only a single response measurement from a free decay test is required as input this ensures that the magnitude of the damping parameters is not compromised by phase distortion between measurements the method uses the instantaneous energy to describe the long term evolution of the system practically this is achieved by using only the peak amplitudes in each period in this way the stiffness is effectively ignored and only the damping forces are considered for this reason the method is not unlike the familiar decrement method which can be used to estimate the apparent linear damping the method is developed in the context of a weakly nonlinear lightly damped system with both linear and cubic damping simulated response data is used to demonstrate the accuracy of the technique the nonlinear damping parameter is extracted from the response data to within 5 of the exact value even though the nonlinear term contributes less than 1 to the total force in the system

stochastic models in population biology and their deterministic analogs we introduce a class of stochastic population models based on patch dynamics the size of the patch may be varied and this allows one to quantify the departures of these stochastic models from various mean field theories which are generally valid as the patch size becomes very large these models may be used to formulate a broad range of biological processes in both spatial and nonspatial contexts here we concentrate on two species competition we present both a mathematical analysis of the patch model in which we derive the precise form of the competition mean field equations and their first order corrections in the nonspatial case and simulation results these mean field equations differ in some important ways from those which are normally written down on phenomenological grounds our general conclusion is that mean field theory is more robust for spatial models than for a single isolated patch this is due to the dilution of stochastic effects in a spatial setting resulting from repeated rescue events mediated by interpatch diffusion however discrete effects due to modest patch sizes lead to striking deviations from mean field theory even in a spatial setting

the path integral analysis of an associative memory model storing an infinite number of finite limit cycles an exact solution of the transient dynamics of an associative memory model storing an infinite number of limit cycles with l finite steps is shown by means of the path integral analysis assuming the maxwell construction ansatz we have succeeded in deriving the stationary state equations of the order parameters from the macroscopic recursive equations with respect to the finite step sequence processing model which has retarded self interactions we have also derived the stationary state equations by means of the signal to noise analysis scsna the signal to noise analysis must assume that crosstalk noise of an input to spins obeys a gaussian distribution on the other hand the path integral method does not require such a gaussian approximation of crosstalk noise we have found that both the signal to noise analysis and the path integral analysis give completely the same result with respect to the stationary state in the case where the dynamics is deterministic when we assume the maxwell construction ansatz we have shown the dependence of the storage capacity c on the number of patterns per one limit cycle l at l 1 the storage capacity is c 0 138 as in the hopfield model the storage capacity monotonically increases with the number of steps and converges to c 0 269 at l 10 the original properties of the finite step sequence processing model appear as long as the number of steps of the limit cycle has order l o 1

random replicators with high order interactions we use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of n species interacting via random mutual interactions as well as via deterministic self interactions of order p 2 we show that the main effect of increasing the order of the interactions among the species is to make the system less competitive in the sense that the fraction of extinct species is greatly reduced in addition we find that for p 2 there is a threshold value which gives a lower bound to the concentration of the surviving species preventing then the existence of rare species and consequently increasing the robustness of the ecosystem to external perturbations

decreasing functions with applications to penalization the theory of increasing positively homogeneous functions defined on the positive orthant is applied to the class of decreasing functions a multiplicative version of the inf convolution operation is studied for decreasing functions modified penalty functions for some constrained optimization problems are introduced that are in general nonlinear with respect to the objective function of the original problem as the perturbation function of a constrained optimization problem is decreasing the theory of decreasing functions is subsequently applied to the study of modified penalty functions the zero duality gap property and the exact penalization

rank abundance relations in evolutionary dynamics of random replicators we present a nonequilibrium statistical mechanics description of rank abundance relations rar in random community models of ecology specifically we study a multispecies replicator system with quenched random interaction matrices we here consider symmetric interactions as well as asymmetric and antisymmetric cases rars are obtained analytically via a generating functional analysis describing fixed point states of the system in terms of a small set of order parameters and in dependence on the symmetry or otherwise of interactions and on the productivity of the community our work is an extension of tokita phys rev lett 93 178102 2004 where the case of symmetric interactions was considered within an equilibrium setup the species abundance distribution in our model come out as truncated normal distributions or transformations thereof and in some case are similar to left skewed distributions observed in ecology we also discuss the interaction structure of the resulting food web of stable species at stationarity cases of heterogeneous cooperation pressures as well as effects of finite system size and of higher order interactions

ecological communities from random generalized lotka volterra dynamics with nonlinear feedback we investigate the outcome of generalized lotka volterra dynamics of ecological communities with random interaction coefficients and nonlinear feedback we show in simulations that the saturation of nonlinear feedback stabilizes the dynamics this is confirmed in an analytical generating functional approach to generalized lotka volterra equations with piecewise linear saturating response for such systems we are able to derive self consistent relations governing the stable fixed point phase and to carry out a linear stability analysis to predict the onset of unstable behavior we investigate in detail the combined effects of the mean variance and covariance of the random interaction coefficients and the saturation value of the nonlinear response we find that stability and diversity increases with the introduction of nonlinear feedback where decreasing the saturation value has a similar effect to decreasing the covariance we also find cooperation to no longer have a detrimental effect on stability with nonlinear feedback and the order parameters mean abundance and diversity to be less dependent on the symmetry of interactions with stronger saturation

a finite dimensional extension of lyusternik theorem with applications to multiobjective optimization abstract we consider a multiobjective program with inequality and equality constraints and a set constraint the equality constraints are frechet differentiable and the objective function and the inequality constraints are locally lipschitz within this context a lyusternik type theorem is extended establishing afterwards both fritz john and kuhn tucker necessary conditions for pareto optimality

np hardness of deciding convexity of quartic polynomials and related problems we show that unless p np there exists no polynomial time or even pseudo polynomial time algorithm that can decide whether a multivariate polynomial of degree four or higher even degree is globally convex this solves a problem that has been open since 1992 when n z shor asked for the complexity of deciding convexity for quartic polynomials we also prove that deciding strict convexity strong convexity quasiconvexity and pseudoconvexity of polynomials of even degree four or higher is strongly np hard by contrast we show that quasiconvexity and pseudoconvexity of odd degree polynomials can be decided in polynomial time

generic minimizing behavior in semialgebraic optimization we present a theorem of sard type for semialgebraic set valued mappings whose graphs have dimension no larger than that of their range space the inverse of such a mapping admits a single valued analytic localization around any pair in the graph for a generic value parameter this simple result yields a transparent and unified treatment of generic properties of semialgebraic optimization problems typical semialgebraic problems have finitely many critical points around each of which they admit a unique active manifold analogue of an active set in nonlinear optimization moreover such critical points satisfy strict complementarity and second order sufficient conditions for optimality are indeed necessary

lagrange multipliers and optimality lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write first order optimality conditions formally as a system of equations modern applications with their emphasis on numerical methods and more complicated side conditions than equations have demanded deeper understanding of the concept and how it fits into a larger theoretical picture a major line of research has been the nonsmooth geometry of one sided tangent and normal vectors to the set of points satisfying the given constraints another has been the game theoretic role of multiplier vectors as solutions to a dual problem interpretations as generalized derivatives of the optimal value with respect to problem parameters have also been explored lagrange multipliers are now being seen as arising from a general rule for the subdifferentiation of a nonsmooth objective function which allows black and white constraints to be replaced by penalty expressions this paper traces su

computing the discrete time analytic signal via fft starting with a real valued n point discrete time signal frequency domain algorithms are provided for computing 1 the complex valued standard n point discrete time analytic signal of the same sample rate 2 the complex valued decimated n 2 point discrete time analytic signal of half the original sample rate and 3 the complex valued interpolated nm point discrete time analytic signal of m times the original sample rate special adjustment of the transform end points are shown to be necessary in order to generate proper discrete time analytic signals

the dimension of semialgebraic subdifferential graphs a b s t r a c t a corollary of a celebrated theorem of minty is that the subdifferential graph of a closed convex function on r n has uniform local dimension n in contrast there exist nonconvex closed functions whose subdifferentials have large graphs we consider how far minty s corollary extends to functions that are nonconvex but semi algebraic

a practical approach to parameter identification for a lightly damped weakly nonlinear system fluidelastic systems are often lightly damped and exhibit weak nonlinear damping the weak linear and nonlinear damping forces have a significant effect on the long term behaviour of the system however parameter identification methods tend to concentrate on identifying the strongest forces in this paper the applicability of two identification methods to a single degree of freedom fluidelastic system is investigated using experimental data the system is weakly nonlinear under flow conditions and is prone to fluidelastic instability i e self excited limit cycle behaviour the crucial effect of the weak damping forces on the system stability and post stable behaviour has been demonstrated the nonlinearity detection and identification has been done using an analytic representation of the displacement signal freevib method and subsequently a nonlinear decrement method was used for comparison the identified models were used to predict the global behaviour of the system in the form of limit cycle amplitudes and this has been used as an indication of accuracy it was found that the nonlinear decrement method yields superior predictions but it suffers from the limitation that the functional form of the system must be known a priori therefore it is concluded that employing both methods together provides a more powerful approach for parameter estimation in a lightly damped system where weak nonlinear damping plays an important role

random replicators with asymmetric couplings systems of interacting random replicators are studied using generating functional techniques while replica analyses of such models are limited to systems with symmetric couplings dynamical approaches as presented here allow us specifically to address cases with asymmetric interactions where there is no lyapunov function governing the dynamics we focus on replicator models with gaussian couplings of general symmetry between p 2 species and discuss how an effective description of the dynamics can be derived in terms of a single species process upon making a fixed point ansatz persistent order parameters in the ergodic stationary states can be extracted from this process and different types of phase transitions can be identified and related to each other we discuss the effects of asymmetry in the couplings on the order parameters and the phase behaviour for p 2 and p 3 numerical simulations verify our theory for the case of cubic interactions numerical experiments indicate regimes in which only a finite number of species survives even when the thermodynamic limit is considered

existence of augmented lagrange multipliers reduction to exact penalty functions and localization principle in this article we present new general results on existence of augmented lagrange multipliers we define a penalty function associated with an augmented lagrangian and prove that under a certain growth assumption on the augmenting function an augmented lagrange multiplier exists if and only if this penalty function is exact we also develop a new general approach to the study of augmented lagrange multipliers called the localization principle the localization principle allows one to study the local behaviour of the augmented lagrangian near global optimal solutions of the initial optimization problem in order to prove the existence of augmented lagrange multipliers

abstract convexity and augmented lagrangians the ultimate goal of this paper is to demonstrate that abstract convexity provides a natural language and a suitable framework for the examination of zero duality gap properties and exact multipliers of augmented lagrangians we study augmented lagrangians in a very general setting and formulate the main definitions and facts describing the augmented lagrangian theory in terms of abstract convexity tools we illustrate our duality scheme with an application to stochastic semi infinite optimization

semi algebraic functions have small subdifferentials we prove that the subdifferential of any semi algebraic extended real valued function on mathbf r n has n dimensional graph we discuss consequences for generic semi algebraic optimization problems

a procrustes problem on the stiefel manifold an orthogonal procrustes problem on the stiefel manifold is studied where a matrix q with orthonormal columns is to be found that minimizes aq b rm f for an l times m matrix a and an l times n matrix b with l geq m and m n based on the normal and secular equations and the properties of the stiefel manifold necessary conditions for a global minimum as well as necessary and sufficient conditions for a local minimum are derived

hamiltonian trajectories and duality in the optimal control of linear systems with convex costs a duality theorem is proved for problems of optimal control of linear dynamical systems in continuous time subject to linear constraints and convex costs such as penalties optimality conditions are stated in terms of a minimaximum principle in which the primal and dual control vectors satisfy a saddle point condition at almost every instant of time this principle is shown to be equivalent to a generalized hamiltonian differential equation in the primal and dual state variables along with a transversality condition that likewise is in hamiltonian form

an augmented lagrangian fish swarm based method for global optimization this paper presents an augmented lagrangian methodology with a stochastic population based algorithm for solving nonlinear constrained global optimization problems the method approximately solves a sequence of simple bound global optimization subproblems using a fish swarm intelligent algorithm a stochastic convergence analysis of the fish swarm iterative process is included numerical results with a benchmark set of problems are shown including a comparison with other stochastic type algorithms

some properties of the augmented lagrangian in cone constrained optimization a large class of optimization problems can be modeled as minimization of an objective function subject to constraints given in a form of set inclusions in this paper we discuss augmented lagrangian duality for such optimization problems we formulate the augmented lagrangian dual problems and study conditions ensuring existence of the corresponding augmented lagrange multipliers we also discuss sensitivity of optimal solutions to small perturbations of augmented lagrange multipliers

a new heuristic approach for non convex optimization problems in this work a new optimization method called the heuristic kalman algorithm hka is presented this new algorithm is proposed as an alternative approach for solving continuous non convex optimization problems the principle of hka is to explicitly consider the optimization problem as a measurement process designed to give an estimate of the optimum a specific procedure based on the kalman estimator was developed to improve the quality of the estimate obtained through the measurement process the main advantage of hka compared to other metaheuristics lies in the small number of parameters that need to be set by the user further it is shown that hka converges almost surely to a near optimal solution the efficiency of hka was evaluated in detail using several non convex test problems both in the unconstrained and constrained cases the results were then compared to those obtained via other metaheuristics the numerical experiments show that hka is a promising approach for solving non convex optimization problems particularly in terms of computation time and success ratio

a fuzzy necessary optimality condition for non lipschitz optimization in asplund spaces in this paper we consider a general optimization problem in the broad class of asplund spaces we derive a new necessary optimality condition in the so called lagrangian fuzzy form without standard lipschitz conditions we also give a chain rule for frechet subdifferentials and subdifferential representations of frechet normals to constrained sets

a non linear investigation of single degree of freedom instability in cylinder arrays subject to cross flow abstract a quasi steady non linear analysis of single degree of freedom motion for a single flexible cylinder in an array of rigid cylinders subject to a fluid cross flow is presented then by using the so called first approximation of krylov and bogoliubov the stability and existence of limit cycle amplitudes are investigated it is shown that in general the stability behaviour predicted by the non linear analysis is in agreement with that obtained from the previously developed linearized analysis the analysis predicts stable limit cycle amplitudes of vibration which increase in magnitude as the velocity is increased also the rate of increase of cylinder vibrational amplitude with velocity is greater for low values of m d 2 than for higher values

quadratic growth and critical point stability of semi algebraic functions we show that quadratic growth of a semi algebraic function is equivalent to strong metric subregularity of the subdifferential a kind of stability of generalized critical points in contrast this equivalence can easily fail outside of the semi algebraic setting as a consequence we derive necessary conditions and sufficient conditions for optimality in subdifferential terms