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

upper semicontinuity of attractors for approximations of semigroups and partial differential equations abstract suppose a given evolutionary equation has a compact attractor and the evolutionary equation is approximated by a finite dimensional system conditions are given to ensure the approximate system has a compact attractor which converges to the original one as the approximation is refined applications are given to parabolic and hyperbolic partial differential equations

a nonlinear programming algorithm based on non coercive penalty functions we consider first the differentiable nonlinear programming problem and study the asymptotic behavior of methods based on a family of penalty functions that approximate asymptotically the usual exact penalty function we associate two parameters to these functions one is used to control the slope and the other controls the deviation from the exact penalty we propose a method that does not change the slope for feasible iterates and show that for problems satisfying the mangasarian fromovitz constraint qualification all iterates will remain feasible after a finite number of iterations the same results are obtained for non smooth convex problems under a slater qualification condition

existence and multiplicity of solutions for asymptotically linear noncooperative elliptic systems abstract using the minimax methods in critical point theory and a generalized landesman lazer type condition we establish two existence results of solutions for asymptotically linear noncooperative elliptic systems at resonance besides this we obtain two solutions in the case of near resonance

a new sequential optimality condition for constrained nonsmooth optimization we introduce a sequential optimality condition for locally lipschitz constrained nonsmooth optimization verifiable just using derivative information and which holds even in the absence of any con

an augmented penalty function method with penalty parameter updates for nonconvex optimization abstract given an augmented lagrangian scheme for a general optimization problem we use an epsilon subgradient step for improving the dual function this can be seen as an update for an augmented penalty method which is more stable because it does not force the penalty parameter to tend to infinity we establish for this update primal dual convergence for our augmented penalty method as illustration we apply our method to the test bed kissing number problem

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

a practically unconditionally gradient stable scheme for the n component cahn hilliard system we present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the n component cahn hilliard system modeling the phase separation of an n component mixture the scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method and the scheme allows us to convert the n component cahn hilliard system into a system of n 1 binary cahn hilliard equations and significantly reduces the required computer memory and cpu time we observe that our numerical solutions are consistent with the linear stability analysis results we also demonstrate the efficiency of the proposed scheme with various numerical experiments

nonlinear augmented lagrangian and duality theory in this paper a unified framework of a nonlinear augmented lagrangian dual problem is investigated for the primal problem of minimizing an extended real valued function by virtue of a nonlinear augmenting penalty function our framework is more general than the ones in the literature in the sense that our nonlinear augmenting penalty function is defined on an open set and that our assumptions are presented in terms of a substitution of the dual variable so our scheme includes barrier penalty functions and the weak peak at zero property as special cases by assuming that the increment of the nonlinear augmenting penalty function with respect to the penalty parameter satisfies a generalized peak at zero property necessary and sufficient conditions for the zero duality gap property are established and the existence of an exact penalty representation is obtained

the zero duality gap property and lower semicontinuity of the perturbation function we examine the validity of the zero duality gap properties for two important dual schemes a generalized augmented lagrangian dual scheme and a nonlinear lagrange type dual scheme the necessary and sufficient conditions for the zero duality gap property to hold are established in terms of the lower semicontinuity of the perturbation functions

systems of cahn hilliard equations the phase separation of alloys with two or more components is studied with emphasis on more than two components particular attention is given to differences between multicomponent and binary alloys specific topics of the paper include equilibrium theory aspects of the dynamics and numerical simulations in the equilibrium theory it is found that there is an enriched equilibrium structure that allows for multiple coexisting phases and the presence of triple points in the solution dynamic results include the characterization of the spinodal region and of the concentration variations that lead to spinodal decomposition unlike the binary theory not all composition variations lead to separation and the compositions are not restricted to the convex hull of the equilibrium concentrations linear analysis is used to predict that a pseudo binary will initially result from spinodal decomposition numerical simulations of the dynamics for a ternary alloy verify this initially but more than two phases often

resonance problems for the p laplacian systems abstract two existence theorems of the solutions are obtained for the p laplacian systems at resonance under a landesman lazer type condition by critical point theory

on the resonance problem with nonlinearity which has arbitrary linear growth abstract this paper deals with the nonlinear two point boundary value problem at resonance even nonlinearities g with an arbitrary linear growth in resp may be considered but only on the cost of the corresponding bound on their linear growth at resp it generalizes the previous results in this direction obtained by m schechter j shapiro and m snow trans amer math soc 241 1978 69 78 l cesari and r kannan proc amer math soc 88 1983 605 613 and s ahmad proc amer math soc 93 1984 381 384

some existence theorems for elliptic resonant problems some existence theorems are obtained for the elliptic resonant problems at either the first eigenvalue or the higher eigenvalues with unbounded nonlinearity by using the minimax methods in critical point theory

a practical numerical scheme for the ternary cahn hilliard system with a logarithmic free energy abstract we consider a practically stable finite difference method for the ternary cahn hilliard system with a logarithmic free energy modeling the phase separation of a three component mixture the numerical scheme is based on a linear unconditionally gradient stable scheme by eyre and is solved by an efficient and accurate multigrid method the logarithmic function has a singularity at zero to remove the singularity we regularize the function near zero by using a quadratic polynomial approximation we perform a convergence test a linear stability analysis and a robustness test of the ternary cahn hilliard equation we observe that our numerical solutions are convergent consistent with the exact solutions of linear stability analysis and stable with practically large enough time steps using the proposed numerical scheme we also study the temporal evolution of morphology patterns during phase separation in one two and three dimensional spaces

solvability of a boundary value problem with the nonlinearity satisfying a sign condition soit f 0 r r une fonction donnee satisfaisant des conditions de caratheodory et h 0 r une fonction donnee dans l 1 0 on obtient l existence d une solution au probleme aux valeurs limites u x u x f x u x h x x 0 u 0 u 0 pour h x telle que 0 h x sinxdx 0 et f x u telle que f x u u 0 pour u r et il y a une constante 0 telle que limsup u f x u u 3 uniformement pour x 0

a unified augmented lagrangian approach to duality and exact penalization in this paper the existence of an optimal path and its convergence to the optimal set of a primal problem of minimizing an extended real valued function are established via a generalized augmented lagrangian and corresponding generalized augmented lagrangian problems in which no convexity is imposed on the augmenting function these results further imply a zero duality gap property between the primal problem and the generalized augmented lagrangian dual problem a necessary and sufficient condition for the exact penalty representation in the framework of a generalized augmented lagrangian is obtained in the context of constrained programs we show that generalized augmented lagrangians present a unified approach to several classes of exact penalization results some equivalences among exact penalization results are obtained

existence and multiplicity of solutions for a class of semilinear elliptic equations the existence and multiplicity results are obtained for solutions of a class of the dirichlet problem for semilinear elliptic equations by the least action principle and the minimax methods respectively

is bilevel programming a special case of a mathematical program with complementarity constraints bilevel programming problems are often reformulated using the karush kuhn tucker conditions for the lower level problem resulting in a mathematical program with complementarity constraints mpcc clearly both problems are closely related but the answer to the question posed is no even in the case when the lower level programming problem is a parametric convex optimization problem this is not obvious and concerns local optimal solutions we show that global optimal solutions of the mpcc correspond to global optimal solutions of the bilevel problem provided the lower level problem satisfies the slater s constraint qualification we also show by examples that this correspondence can fail if the slater s constraint qualification fails to hold at lower level when we consider the local solutions the relationship between the bilevel problem and its corresponding mpcc is more complicated we also demonstrate the issues relating to a local minimum through examples

convergence of the gradient sampling algorithm for nonsmooth nonconvex optimization we study the gradient sampling algorithm of burke lewis and overton for minimizing a locally lipschitz function f on mathbb r n that is continuously differentiable on an open dense subset we strengthen the existing convergence results for this algorithm and introduce a slightly revised version for which stronger results are established without requiring compactness of the level sets of f in particular we show that with probability 1 the revised algorithm either drives the f values to infty or each of its cluster points is clarke stationary for f we also consider a simplified variant in which the differentiability check is skipped and the user can control the number of f evaluations per iteration

resonance problems for the p laplacian with a nonlinear boundary condition abstract consider resonance problems at an arbitrary eigenvalue of the elliptic equations p u u p 2 u g 1 u h 1 x in u p 2 u u p 2 u g 2 u h 2 x on some existence theorems are obtained under the landesman lazer type conditions by using variational method

a linesearch based derivative free approach for nonsmooth constrained optimization in this paper we propose new linesearch based methods for nonsmooth constrained optimization problems when first order information on the problem functions is not available in the first part we describe a general framework for bound constrained problems and analyze its convergence toward stationary points using the clarke jahn directional derivative in the second part we consider inequality constrained optimization problems where both objective function and constraints can possibly be nonsmooth in this case we first split the constraints into two subsets difficult general nonlinear constraints and simple bound constraints on the variables then we use an exact penalty function to tackle the difficult constraints and we prove that the original problem can be reformulated as the bound constrained minimization of the proposed exact penalty function finally we use the framework developed for the bound constrained case to solve the penalized problem moreover we prove that every accumulation poin

second order schemes and time step adaptivity for allen cahn and cahn hilliard models abstract in this paper we focus on efficient second order in time approximations of the allen cahn and cahn hilliard equations first of all we present the equations generic second order schemes based on a mid point approximation of the diffusion term and some schemes already introduced in the literature then we propose new ways of deriving second order in time approximations of the potential term starting from the main schemes introduced in guillen gonzalez and tierra 2013 yielding to new second order schemes for these schemes and other second order schemes previously introduced in the literature we study the constraints on the physical and discrete parameters that can appear to assure the energy stability unique solvability and in the case of nonlinear schemes the convergence of newton s method to the nonlinear schemes moreover in order to save computational cost we have developed a new adaptive time stepping algorithm based on the numerical dissipation introduced in the discrete energy law in each time step finally we compare the behaviour of the schemes and the effectiveness of the adaptive time stepping algorithm through several computational experiments

on the convergence of augmented lagrangian methods for constrained global optimization in this paper we present new convergence properties of the primal dual method based on four types of augmented lagrangian functions in the context of constrained global optimization convergence to a global optimal solution is first established for a basic primal dual scheme under standard conditions we then prove this convergence property for a modified augmented lagrangian method using a safeguarding strategy without appealing to the boundedness assumption of the multiplier sequence we further show that under the same weaker conditions the convergence to a global optimal solution can still be achieved by either modifying the multiplier updating rule or normalizing the multipliers in augmented lagrangian methods

the numerical computation of heteroclinic connections in systems of gradient partial differential equations the numerical computation of heteroclinic connections in partial differential equations pdes with a gradient structure such as those arising in the modeling of phase transitions is considered initially a scalar reaction diffusion equation is studied structural assumptions are made on the problem to ensure the existence of absorbing sets and consequently a global attractor as a result of the gradient structure it is known that if all equilibria are hyperbolic the global attractor comprises the set of equilibria and heteroclinic orbits connecting equilibria to one another thus it is natural to consider direct approximation of the set of equilibria and the connecting orbits results are proved about the fourier spanning basis for branches of equilibria and also for certain heteroclinic connections these results exploit the oddness of the nonlinearity the reaction diffusion equation is then approximated by a galerkin spectral discretization to produce a system of ordinary differential equations

multiple solutions for semilinear elliptic equations near resonance at higher eigenvalues abstract using the minimax methods in critical point theory and a generalized landesman lazer type condition we obtain two solutions for a class of semilinear elliptic equations near resonance at higher eigenvalues

an error bound for the finite element approximation of the cahn hilliard equation with logarithmic free energy an error bound is proved for a fully practical piecewise linear finite element approximation using a backward euler time discretization of the cahn hilliard equation with a logarithmic free energy

efficient numerical solution of discrete multi component cahn hilliard systems in this work we develop preconditioners for the iterative solution of the large scale algebraic systems arising in finite element discretizations of microstructures with an arbitrary number of components described by the diffusive interface model the suggested numerical techniques are applied to the study of ternary fluid flow processes

solvability for two point boundary value problems abstract suppose that h l 1 0 g c r r and lim t g t t 0 with the saddle point theorem the solvability is proved for the two point boundary value problemproblem formula under the condition that formula where formula and formula

the global dynamics of discrete semilinear parabolic equations a class of scalar semilinear parabolic equations possessing absorbing sets a lyapunov functional and a global attractor are considered the gradient structure of the problem implies that provided all steady states are isolated solutions approach a steady state as t to infty the dynamical properties of various finite difference and finite element schemes for the equations are analysed the existence of absorbing sets bounded independently of the mesh size is proved for the numerical methods discrete lyapunov functions are constructed to show that under appropriate conditions on the mesh parameters numerical orbits approach steady state solutions as discrete time increases however it is shown that insufficient spatial resolution can introduce deceptively smooth spurious steady solutions and cause the stability properties of the true steady solutions to be incorrectly represented furthermore it is also shown that the explicit euler scheme introduces spurious solutions with period 2 in the timestep as a result the absorbing set is destroyed and there is initial data leading to blow up of the scheme however small the mesh parameters are taken to obtain stabilization to a steady state for this scheme it is necessary to restrict the timestep in terms of the initial data and the space step implicit schemes are constructed for which absorbing sets and lyapunov functions exist under restrictions on the timestep that are independent of initial data and of the space step both one step and multistep bdf methods are studied

a robust gradient sampling algorithm for nonsmooth nonconvex optimization let f be a continuous function on rl n and suppose f is continuously differentiable on an open dense subset such functions arise in many applications and very often minimizers are points at which f is not differentiable of particular interest is the case where f is not convex and perhaps not even locally lipschitz but is a function whose gradient is easily computed where it is defined we present a practical robust algorithm to locally minimize such functions based on gradient sampling no subgradient information is required by the algorithm when f is locally lipschitz and has bounded level sets and the sampling radius eps is fixed we show that with probability 1 the algorithm generates a sequence with a cluster point that is clarke eps stationary furthermore we show that if f has a unique clarke stationary point bar x then the set of all cluster points generated by the algorithm converges to bar x as eps is reduced to zero numerical results are presented demonstrating the robustness of the algorithm and its applicability in a wide variety of contexts including cases where f is not locally lipschitz at minimizers we report approximate local minimizers for functions in the applications literature which have not to our knowledge been obtained previously when the termination criteria of the algorithm are satisfied a precise statement about nearness to clarke eps stationarity is available a matlab implementation of the algorithm is posted at http www cs nyu edu overton papers gradsamp alg

finite element approximation of a model for phase separation of a multi component alloy with non smooth free energy a model for the phase separation of a multi component alloy with non smooth free energy is considered an error bound is proved for a fully practical piecewise linear finite element approximation using a backward euler time discretization an iterative scheme for solving the resulting nonlinear algebraic system is analysed finally numerical experiments with three components in one and two space dimensions are presented in the one dimensional case we compare some steady states obtained numerically with the corresponding stationary solutions of the continuous problem which we construct explicitly

exact augmented lagrangian duality for mixed integer linear programming we investigate the augmented lagrangian dual ald for mixed integer linear programming mip problems ald modifies the classical lagrangian dual by appending a nonlinear penalty function on the violation of the dualized constraints in order to reduce the duality gap we first provide a primal characterization for ald for mips and prove that ald is able to asymptotically achieve zero duality gap when the weight on the penalty function is allowed to go to infinity this provides an alternative characterization and proof of a recent result in boland and eberhard math program 150 2 491 509 2015 proposition 3 we further show that under some mild conditions ald using any norm as the augmenting function is able to close the duality gap of an mip with a finite penalty coefficient this generalizes the result in boland and eberhard 2015 corollary 1 from pure integer programming problems with bounded feasible region to general mips we also present an example where ald with a quadratic augmenting function is not able to close the duality gap for any finite penalty coefficient

strongly resonant quasilinear elliptic equations abstract in this paper we study the following nonlinear boundary value problem p u 1 u p 2 u g u in u 0 an existence result is shown under some strong resonance conditions generalizing those of tang and landesman lazer

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

efficient energy stable numerical schemes for a phase field moving contact line model in this paper we present two efficient energy stable schemes to solve a phase field model incorporating moving contact line the model is a coupled system that consists of incompressible navier stokes equations with a generalized navier boundary condition and cahn hilliard equation in conserved form in both schemes the projection method is used to deal with the navier stokes equations and stabilization approach is used for the non convex ginzburg landau bulk potential by some subtle explicit implicit treatments we obtain a linear coupled energy stable scheme for systems with dynamic contact line conditions and a linear decoupled energy stable scheme for systems with static contact line conditions an efficient spectral galerkin spatial discretization method is implemented to verify the accuracy and efficiency of proposed schemes numerical results show that the proposed schemes are very efficient and accurate we proposed two linear energy stable numerical schemes for a phase field moving contact line model discrete energy laws that are consistent to the continuous ones are proved the efficiency and fast convergence of the proposed schemes with spectral spatial approximations are numerically verified

a boundary value problem with a periodic nonlinearity soit g r r une fonction continue et periodique de periode t 0 et soit h l 1 0 on considere le probleme d existence pour le probleme aux limites de picard u u g u h u 0 0 u

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

on anisotropic order parameter models for multi phase system and their sharp interface limits abstract for a general class of diffuse anisotropic multi phase order parameter or phase field models we use formally matched asymptotic expansions to determine the asymptotic limit when a small parameter related to the thickness of the interface tends to zero in the case of anisotropic allen cahn systems we obtain in the limit that the interface moves by anisotropic mean curvature flow at triple junctions a force balance holds which in the anisotropic case includes shear forces herring torque terms acting normal to the interface we further identify the singular limit of anisotropic cahn hilliard systems

runge kutta methods for dissipative and gradient dynamical systems the numerical approximation of dissipative initial value problems by fixed time stepping runge kutta methods is considered and the asymptotic features of the numerical and exact solutions are compared a general class of ordinary differential equations for which dissipativity is induced through an inner product is studied throughout this class arises naturally in many finite dimensional applications such as the lorenz equations and also from the spatial discretization of a variety of partial differential equations arising in applied mathematics it is shown that the numerical solution defined by an algebraically stable method has an absorbing set and is hence dissipative for any fixed step size h 0 the numerical solution is shown to define a dynamical system on the absorbing set if h is sufficiently small and hence a global attractor a h exists upper semicontinuity of a h at h 0 is established which shows that for h small every point on the numerical attractor is close to a point on the true global attractor a under the additional assumption that the problem is globally lipschitz it is shown that if h is sufficiently small any method with positive weights defines a dissipative dynamical system on the whole space and upper semicontinuity of a h at h 0 is again established for gradient systems with globally lipschitz vector fields it is shown that any runge kutta method preserves the gradient structure for h sufficiently small for general dissipative gradient systems it is shown that algebraically stable methods preserve the gradient structure within the absorbing set for h sufficiently small convergence of the numerical attractor is studied and for a dissipative gradient system with hyperbolic equilibria lower semicontinuity at h 0 is established thus for such a system a h converges to a in the hausdorff metric as h 0

exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization this paper presents new versions of proximal bundle methods for solving convex constrained nondifferentiable minimization problems the methods employ 1 or exact penalty functions with new penalty updates that limit unnecessary penalty growth in contrast to other methods some of them are insensitive to problem function scaling global convergence of the methods is established as well as finite termination for polyhedral problems some encouraging numerical experience is reported the ideas presented may also be used in variable metric methods for smooth nonlinear programming

on saddle points of augmented lagrangians for constrained nonconvex optimization we present in this paper new results on the existence of saddle points of augmented lagrangian functions for constrained nonconvex optimization four classes of augmented lagrangian functions are considered the essentially quadratic augmented lagrangian the exponential type augmented lagrangian the modified barrier augmented lagrangian and the penalized exponential type augmented lagrangian we first show that under second order sufficiency conditions all these augmented lagrangian functions possess local saddle points we then prove that global saddle points of these augmented lagrangian functions exist under certain mild additional conditions the results obtained in this paper provide a theoretical foundation for the use of augmented lagrangians in constrained global optimization our findings also give new insights to the role played by augmented lagrangians in local duality theory of constrained nonconvex optimization

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

strong resonance for some quasilinear elliptic equations abstract we study the existence of the weak solutions of the nonlinear boundary value problem p u 1 u p 2 u g u h x in u 0 on where the nonlinearity g is of the landesman lazer type our sufficient conditions generalize all previously published results about the strong resonance at the first eigenvalue

remarks on existence and multiplicity of solutions for a class of semilinear elliptic equations the existence and multiplicity results are obtained for solutions of a class of the dirichlet problem for semilinear elliptic equations by the least action principle and the minimax methods respectively

a new sequential optimality condition for constrained optimization and algorithmic consequences necessary first order sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constraint qualifications a new condition of this type is introduced in the present paper it is proved that a well established augmented lagrangian algorithm produces sequences whose limits satisfy the new condition practical consequences are discussed

a novel linear unconditional energy stable scheme for the incompressible cahn hilliard navier stokes phase field model abstract in this paper we propose a linear unconditional energy stable time discretization scheme for cahn hilliard navier stokes model which is a phase field model for two phase incompressible flow based on a lagrange multiplier approach our proposed scheme is linearized by using implicit explicit treatments and the computation of the velocity field u the pressure p the phase function are decoupled using the mathematical induction the bound n l is obtained rigorous error analysis for the variable u p and are carried out in semi discrete form finally some numerical experiments are done to demonstrate the effectiveness for the proposed method

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