a new nonmonotone line search technique for unconstrained optimization in this paper we propose a new nonmonotone line search technique for unconstrained optimization problems by using this new technique we establish the global convergence under conditions weaker than those of the existed nonmonotone line search techniques

cauchy problem for the multi dimensional boussinesq type equation abstract the paper studies the existence and non existence of global weak solutions to the cauchy problem for the multi dimensional boussinesq type equation u t t u 2 u u it proves that the cauchy problem admits a global weak solution under the assumptions that c r s is of polynomial growth order say p 1 either 0 s s 0 s d s r where 0 is a constant or the initial data belong to a potential well and the weak solution is regularized and the strong solution is unique when the space dimension n 1 in contrast any weak solution of the cauchy problem blows up in finite time under certain conditions and two examples are shown

an ode based trust region method for unconstrained optimization problems in this paper a new trust region algorithm is proposed for solving unconstrained optimization problems this method can be regarded as a combination of trust region technique fixed step length and ode based methods a feature of this proposed method is that at each iteration only a system of linear equations is solved to obtain a trial step another is that when a trial step is not accepted the method generates an iterative point whose step length is defined by a formula under some standard assumptions it is proven that the algorithm is globally convergent and locally superlinear convergent preliminary numerical results are reported

nonmonotone algorithm for minimax optimization problems many real life problems can be stated as a minimax optimization problem such as the problems in economics finance management engineering and other fields in this paper we present an algorithm with nonmonotone strategy and second order correction technique for minimax optimization problems using this scheme the new algorithm can overcome the difficulties of the maratos effect occurred in the nonsmooth optimization and the global and superlinear convergence of the algorithm can be achieved accordingly numerical experiments indicate some advantages of this scheme

a nonmonotone trust region method based on nonincreasing technique of weighted average of the successive function values in this paper we propose a nonmonotone trust region method unlike traditional nonmonotone trust region method the nonmonotone technique applied to our method is based on the nonmonotone line search technique proposed by zhang and hager a nonmonotone line search technique and its application to unconstrained optimization siam j optim 14 4 2004 1043 1056 instead of that presented by grippo et al a nonmonotone line search technique for newton s method siam j numer anal 23 4 1986 707 716 so the method requires nonincreasing of a special weighted average of the successive function values global and superlinear convergence of the method are proved under suitable conditions preliminary numerical results show that the method is efficient for unconstrained optimization problems

nonmonotone gradient methods for vector optimization with a portfolio optimization application abstract this paper proposes two nonmonotone gradient algorithms for a class of vector optimization problems with a c convex objective function we establish both the global and local convergence results for the new algorithms we then apply the new algorithms to a portfolio optimization problem under multi criteria considerations

global convergence of nonmonotone descent methods for unconstrained optimization problems global convergence results are established for unconstrained optimization algorithms that utilize a nonmonotone line search procedure this procedure allows the user to specify a flexible forcing function and includes the nonmonotone armijo rule the nonmonotone goldstein rule and the nonmonotone wolfe rule as special cases

global existence and blow up of solutions for cauchy problem of generalized boussinesq equation abstract we study the cauchy problem of generalized boussinesq equation u t t u x x u x x f u x x 0 where f u u p or u p 1 u p 1 by introducing a family of potential wells we obtain invariant sets vacuum isolating and threshold result of global existence and nonexistence of solution

a nonmonotone adaptive trust region method and its convergence abstract in this paper we combine the new trust region subproblem proposed in 1 with the nonmonotone technique to propose a new algorithm for unconstrained optimization the nonmonotone adaptive trust region method the local and global convergence properties of the nonmonotone adaptive trust region method are proved its efficiency is tested by numerical results

global existence of smooth solutions and stability of solitary waves for a generalized boussinesq equation certain generalizations of one of the classical boussinesq type equations u tt u xx u 2 u xx xx are considered it is shown that the initial value problem for this type of equation is always locally well posed it is also determined that the special solitary wave solutions of these equations are nonlinearly stable for a range of their phase speeds these two facts lead to the conclusion that initial data lying relatively close to a stable solitary wave evolves into a global solution of these equations this contrasts with the results of blow up obtained recently by kalantarov and ladyzhenskaya for the same type of equation and casts additional light upon the results for the original version of this class of equations obtained via inverse scattering theory by deift tomei and trubowitz

non monotone trust region algorithms for nonlinear optimization subject to convex constraints this paper presents two new trust region methods for solving nonlinear optimization problems over convex feasible domains these methods are distinguished by the fact that they do not enforce strict monotonicity of the objective function values at successive iterates the algorithms are proved to be convergent to critical points of the problem from any starting point extensive numerical experiments show that this approach is competitive with the lancelot package

local and global existence of solutions for the cauchy problem of a generalized boussinesq equation abstract we consider the local and global existence of solutions for a generalized boussinesq equation u t t u x x u x x x x u k 1 x x 0 k 4 with initial data in some homogenous besov type space

an adaptive nonmonotone trust region method with curvilinear search for minimax problem in this paper we propose an adaptive nonmonotone algorithm for minimax problem unlike traditional nonmonotone method the nonmonotone technique applied to our method is based on the nonmonotone technique proposed by zhang and hager h c zhang w w hager a nonmonotone line search technique and its application to unconstrained optimization siam j optim 14 4 2004 1043 1056 instead of that presented by grippo et al l grippo f lampariello s lucidi a nonmonotone line search technique for newton s method siam j numer anal 23 4 1986 707 716 meanwhile by using adaptive technique it can adaptively perform the nonmonotone trust region step or nonmonotone curvilinear search step when the solution of subproblems is unacceptable global and superlinear convergences of the method are obtained under suitable conditions preliminary numerical results are reported to show the effectiveness of the proposed algorithm

a modified sqp method with nonmonotone technique and its global convergence in this paper we propose a modified sqp method which uses neither a penalty function nor a filter for the nonlinear programming problems the proposed mechanism for accepting the trial step is carried out by a nonmonotone technique under some conditions we establish the global convergence of the algorithm some numerical results are presented to show the effectiveness of the proposed algorithm

a new nonmonotone trust region method of conic model for solving unconstrained optimization in this paper we present a new nonmonotone trust region method of conic model for solving unconstrained optimization problems both the local and global convergence properties are analyzed under reasonable assumptions numerical experiments are conducted to compare this method with some existed ones which indicate that the new method is efficient

soliton and antisoliton interactions in the good boussinesq equation the solitary wave interaction mechanism for the good boussinesq equation is investigated and found to be far more complicated than was previously thought three salient features are that solitary waves only exist for a finite range of velocities that large solitons can turn into so called antisolitons and that it is possible for solitons to merge and split small solitons however appear to be stable the existence of a potential well is linked to the different behaviors observed between small and large initial conditions

a new active set algorithm for box constrained optimization an active set algorithm asa for box constrained optimization is developed the algorithm consists of a nonmonotone gradient projection step an unconstrained optimization step and a set of rules for branching between the two steps global convergence to a stationary point is established for a nondegenerate stationary point the algorithm eventually reduces to unconstrained optimization without restarts similarly for a degenerate stationary point where the strong second order sufficient optimality condition holds the algorithm eventually reduces to unconstrained optimization without restarts a specific implementation of the asa is given which exploits the recently developed cyclic barzilai borwein cbb algorithm for the gradient projection step and the recently developed conjugate gradient algorithm cg descent for unconstrained optimization numerical experiments are presented using box constrained problems in the cuter and minpack 2 test problem libraries

global convergence of the nonmonotone mbfgs method for nonconvex unconstrained minimization in this paper we propose a new nonmonotone armijo type line search and prove that the mbfgs method proposed by li and fukushima with this new line search converges globally for nonconvex minimization some numerical experiments show that this nonmonotone mbfgs method is efficient for the given test problems

an assessment of nonmonotone linesearch techniques for unconstrained optimization the purpose of this paper is to discuss the potential of nonmonotone techniques for enforcing convergence of unconstrained minimization algorithms from starting points distant from the solution linesearch based algorithms are considered for both small and large problems and extensive numerical experiments show that this potential is sometimes considerable a new variant is introduced in order to limit some of the identified drawbacks of the existing techniques this variant is again numerically tested and appears to be competitive finally the impact of preconditioning on the considered methods is examined

well posedness of the good boussinesq equation in analytic gevrey spaces and time regularity abstract the cauchy problem for the good boussinesq equation with data in analytic gevrey spaces on the line and the circle is considered and its local well posedness in these spaces is proved the proof is based on bilinear estimates in bourgain type spaces incorporating the symbol of the linear part of the equation and an exponential weight expressing the analytic gevrey regularity of the solution in the spatial variable also gevrey regularity of the solution in time variable is provided

spectral analysis for automorphisms of uhf c algebras abstract we study outer conjugacy for aperiodic automorphisms of uhf c algebras we show the existence of an action on the universal uhf algebra which is absorbing via tensor product for product actions we provide an explicit criterion for the action to be absorbing this criterion involves the eventual uniform distribution mod 1 of the eigenvalues of the approximating unitaries

on the cauchy problem for a generalized boussinesq equation in this paper we consider the cauchy problem for a generalized boussinesq equation we show that under suitable conditions a global solution for the initial value problem exists in addition we derive the sufficient conditions for the blow up of the solution to the problem

incorporating nonmonotone strategies into the trust region method for unconstrained optimization this paper concerns a nonmonotone line search technique and its application to the trust region method for unconstrained optimization problems in our line search technique the current nonmonotone term is a convex combination of the previous nonmonotone term and the current objective function value instead of an average of the successive objective function values that was introduced by zhang and hager h zhang w w hager a nonmonotone line search technique and its application to unconstrained optimization siam j optim 14 4 2004 1043 1056 we incorporate this nonmonotone scheme into the traditional trust region method such that the new algorithm possesses nonmonotonicity unlike the traditional trust region method our algorithm performs a nonmonotone line search to find a new iteration point if a trial step is not accepted instead of resolving the subproblem under mild conditions we prove that the algorithm is global and superlinear convergence holds primary numerical results are reported

efficient line search methods for convex functions in this paper we propose two new line search methods for convex functions these new methods exploit the convexity property of the function contrary to existing methods the first method is an improved version of the golden section method for the second method it is proven that after two evaluations the objective gap is at least halved the practical efficiency of the methods is shown by applying our methods to a real life bus and buffer size optimization problem and to several classes of convex functions

nonmonotone trust region method for solving optimization problems in this paper a trust region tr method with nonmonotone technique for optimization is proposed we construct a new ratio of actual descent and predicted descent which is a simple and natural generalization of the modified armijo line search rule the paper exposes the relationship between the trust region method and line search approach since this method possesses the robust properties of trust region subproblem it is globally convergent although we employ the nonmonotone sequence of function values instead of the monotone sequence in addition the proof of convergence is obviously simpler than one of newton type method with nonmonotone line search finally applications of the nonmonotone tr algorithm to some optimization problems are discussed

stability for integer actions on uhf c algebras on montre qu il est possibile d obtenir une version norme continue de la solution de connes a la 1 cohomologie qui est adaptable a la situation des c algebres on exhibe diverses actions modeles stables

numerical research on the sensitivity of nonmonotone trust region algorithms to their parameters in this paper a numerical research on the sensitivity of nonmonotone trust region algorithms to their parameters is presented we compare the numerical efficiency of two classes of nonmonotone trust region ntr algorithms in the context of unconstrained optimization we examine the sensitivity of the algorithms to the parameters related to the nonmonotone technique and the initial trust region radius we show that the numerical efficiency of nonmonotone trust region algorithms can be improved by choosing appropriate parameters based on extensive numerical tests some efficient ranges of these parameters for nonmonotone trust region algorithms are recommended

inviscid limit for the damped boussinesq equation abstract in this paper we consider the limit behavior of solutions to the cauchy problem for damped boussinesq equation in the regime of small viscosity in r n it is shown that the strong solutions of damped boussinesq equation converge to a strong solution of boussinesq equation in any time interval 0 t the key idea is that we only take into account the effect of dispersion and overlook the effect of dissipation in the damped boussinesq equation which is a kind of new view we analyze the dispersion by the techniques of high low frequency decomposition and littlewood paley dyadic decomposition stationary phase estimate and some properties of bessel function

trust region algorithm for nonsmooth optimization minimization of a composite function h f x is considered here where f r n r m is a locally lipschitzian function and h r m r is a continuously differentiable convex function theory of trust region algorithm for nonsmooth optimization given by fletcher powell and yuan is extended to this case trust region algorithm and its global convergence are studied finally some applications on nonlinear and nonsmooth least squares problems are also given

decay estimates for a class of wave equations abstract in this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by e i t where r r is smooth away from the origin especially the decay estimates for the solutions of the klein gordon equation and the beam equation are simplified and slightly improved

spectral residual methods with two new non monotone line searches for large scale nonlinear systems of equations in this study we develop two new non monotone line searches and combine them into a spectral residual method furthermore we apply these methods to complementary problems and discuss global convergence under several suitable conditions numerical experiments support the efficiency of the presented methods

a fast algorithm for sparse reconstruction based on shrinkage subspace optimization and continuation we propose a fast algorithm for solving the ell 1 regularized minimization problem min x in mathbb r n mu x 1 ax b 2 2 for recovering sparse solutions to an undetermined system of linear equations ax b the algorithm is divided into two stages that are performed repeatedly in the first stage a first order iterative shrinkage method yields an estimate of the subset of components of x likely to be nonzero in an optimal solution restricting the decision variables x to this subset and fixing their signs at their current values reduces the ell 1 norm x 1 to a linear function of x the resulting subspace problem which involves the minimization of a smaller and smooth quadratic function is solved in the second phase our code fpc as embeds this basic two stage algorithm in a continuation homotopy approach by assigning a decreasing sequence of values to mu this code exhibits state of the art performance in terms of both its speed and its ability to recover sparse signals

nonstable solitons and sharp criteria for wave collapse sharp sufficient criteria for collapse are found for the nonlinear schr odinger equation in the so called supercritical case as well as for the ginzburg landau equation in the case of the subcritical bifurcation it is demonstrated that nonstable solitons in these models under some additional assumptions play the role of a boundary saddle points between collapsing and noncollapsing solutions

a nonmonotone trust region method with adaptive radius for unconstrained optimization problems in this paper we incorporate a nonmonotone technique with the new proposed adaptive trust region radius shi and guo 2008 4 in order to propose a new nonmonotone trust region method with an adaptive radius for unconstrained optimization both the nonmonotone techniques and adaptive trust region radius strategies can improve the trust region methods in the sense of global convergence the global convergence to first and second order critical points together with local superlinear and quadratic convergence of the new method under some suitable conditions numerical results show that the new method is very efficient and robustness for unconstrained optimization problems

a globally convergent bfgs method with nonmonotone line search for non convex minimization in this paper we propose a modified bfgs broyden fletcher goldfarb shanno method with nonmonotone line search for unconstrained optimization under some mild conditions we show that the method is globally convergent without a convexity assumption on the objective function we also report some preliminary numerical results to show the efficiency of the proposed method

strong instability of solitary wave solutions of a generalized boussinesq equation abstract in this paper we prove the strong instability of solitary wave solutions with small speed of propagation for a generalized boussinesq equation

nonmonotone bfgs trained recurrent neural networks for temporal sequence processing in this paper we propose a nonmonotone approach to recurrent neural networks training for temporal sequence processing applications this approach allows learning performance to deteriorate in some iterations nevertheless the network s performance is improved over time a self scaling bfgs is equipped with an adaptive nonmonotone technique that employs approximations of the lipschitz constant and is tested on a set of sequence processing problems simulation results show that the proposed algorithm outperforms the bfgs as well as other methods previously applied to these sequences providing an effective modification that is capable of training recurrent networks of various architectures

an extended nonmonotone line search technique for large scale unconstrained optimization abstract in this paper an extended nonmonotone line search is proposed to improve the efficiency of the existing line searches this line search is first proved to be an extension of the classical line search rules on the one hand under mild assumptions global convergence and r linear convergence are established for the new line search rule on the other hand by numerical experiments it is shown that the line search can integrate the advantages of the existing methods in searching for a suitable step size combined with the spectral step size a class of spectral gradient algorithms are developed and employed to solve a large number of benchmark test problems from cutest numerical results show that the new line search is promising in solving large scale optimization problems and outperforms the other similar ones as it is combined with a spectral gradient method

nonmonotone second order wolfe s line search method for unconstrained optimization problems in this paper we present a new algorithm using the nonmonotone second order wolfe s line search by using the negative curvature information from the hessian we prove that the generated sequence converges to the stationary points that satisfy the second order optimality conditions we also report numerical results which show the efficiency and robustness of the proposed method

the convergence of conjugate gradient method with nonmonotone line search abstract the conjugate gradient method is a useful and powerful approach for solving large scale minimization problems liu and storey developed a conjugate gradient method which has good numerical performance but no global convergence under traditional line searches such as armijo line search wolfe line search and goldstein line search in this paper we propose a new nonmonotone line search for liu storey conjugate gradient method ls in short the new nonmonotone line search can guarantee the global convergence of ls method and has a good numerical performance by estimating the lipschitz constant of the derivative of objective functions in the new nonmonotone line search we can find an adequate step size and substantially decrease the number of functional evaluations at each iteration numerical results show that the new approach is effective in practical computation

a nonmonotone line search technique and its application to unconstrained optimization a new nonmonotone line search algorithm is proposed and analyzed in our scheme we require that an average of the successive function values decreases while the traditional nonmonotone approach of grippo lampariello and lucidi siam j numer anal 23 1986 pp 707 716 requires that a maximum of recent function values decreases we prove global convergence for nonconvex smooth functions and r linear convergence for strongly convex functions for the l bfgs method and the unconstrained optimization problems in the cute library the new nonmonotone line search algorithm used fewer function and gradient evaluations on average than either the monotone or the traditional nonmonotone scheme

a rohlin property for one parameter automorphism groups we define a rohlin property for one parameter automorphism groups of unital simplec algebras and show that for such an automorphism group any cocycle is almost a coboundary we apply the same method to the single automorphism case and show that if an automorphism of a unital simplec algebra with a certain condition has a central sequence of approximate eigen unitaries for any complex number of modulus one then any cocycle is almost a coboundary or the automorphism has the stability we also show that if a one parameter automorphism group of a unital separable purely infinite simplec algebra has the rohlin property then the crossed product is simple and purely infinite

nonmonotone algorithm for minimization on closed sets with applications to minimization on stiefel manifolds a nonmonotone levenberg marquardt based algorithm is proposed for minimization problems on closed domains by preserving the feasible set s geometry throughout the process the method generates a feasible sequence converging to a stationary point independently of the initial guess as an application a specific algorithm is derived for minimization on stiefel manifolds and numerical results involving a weighted orthogonal procrustes problem are reported

nonmonotone adaptive trust region method for unconstrained optimization problems in this paper an adaptive trust region method with nonmonotone technique for unconstrained optimization problems is presented and analyzed the global and local convergence results of the algorithm are established numerical results show that the new method is efficient

decay and scattering of small solutions of a generalized boussinesq equation abstract we study the long time behavior of small solutions of the initial value problem for a generalized boussinesq equation we obtain a lower bound for the degrees of nonlinearity which allows us to establish a nonlinear scattering result for small perturbations that is the small solutions of the nonlinear problem behave asymptotically like the solution of the associated linear problem under certain hypotheses we can construct a scattering operator for the boussinesq equation which carries a neighborhood of 0 in the energy space x into x

line search methods with guaranteed asymptotical convergence to an improving local optimum of multimodal functions abstract this paper considers line search optimization methods using a mathematical framework based on the simple concept of a v pattern and its properties this framework provides theoretical guarantees on preserving in the localizing interval a local optimum no worse than the starting point notably the framework can be applied to arbitrary unidimensional functions including multimodal and infinitely valued ones enhanced versions of the golden section bisection and brent s methods are proposed and analyzed within this framework they inherit the improving local optimality guarantee under mild assumptions the enhanced algorithms are proved to converge to a point in the solution set in a finite number of steps or that all their accumulation points belong to the solution set

decay estimates for a dissipative dispersive linear semigroup and application to the viscous boussinesq equation abstract at the core of this article is the new estimate for a class of dissipative dispersive linear semigroup e t i p t arising in the study of the viscous boussinesq equation we combine the decay estimate with introducing a set of time weighted sobolev spaces where the time weights and the regularity of the sobolev spaces are determined by our decay estimate to show the global existence and asymptotic behavior of solutions to the viscous boussinesq equation in r n

existence and scattering theory for boussinesq type equations with singular data we study the initial value problem for the generalized boussinesq equation and prove existence of local and global solutions with singular initial data in weak lp spaces our class of initial data for global existence is larger than that of cho and ozawa 2007 7 long time behavior results are obtained and a scattering theory is proved in that framework with more structure we show sobolev h1 and lorentz type l p q regularity properties for the obtained solutions the approach employed is unified for all dimensions n 1

convergence of descent method without line search line search method is sometimes a useful and efficient technique for solving unconstrained optimization problems especially for solving small and middle scale problems however a line search procedure is necessary at each iteration leading to a significant amount of computation in order to reduce the evaluations of objective functions and gradients the line search procedure should be avoided in algorithm design in this paper we propose a new descent method without line search for unconstrained optimization problems the algorithm is required to estimate some parameters at each iteration we analyze theoretically the global convergence of the new algorithm under mild conditions these theoretical conclusions can help us in designing new efficient methods for optimization problems

a new family of conjugate gradient methods in this paper we develop a new class of conjugate gradient methods for unconstrained optimization problems a new nonmonotone line search technique is proposed to guarantee the global convergence of these conjugate gradient methods under some mild conditions in particular polak ribiere polyak and liu storey conjugate gradient methods are special cases of the new class of conjugate gradient methods by estimating the local lipschitz constant of the derivative of objective functions we can find an adequate step size and substantially decrease the function evaluations at each iteration numerical results show that these new conjugate gradient methods are effective in minimizing large scale non convex non quadratic functions