on identification of active constraints ii the nonconvex case in this paper the results of burke and more 5 on the identification of active constraints are extended to the nonconvex constrained nonlinear programming problem the approach is motivated by the geometric structure of a certain polyhedral convex linearization of the constraint region at each iteration as in burke and more 5 questions of constraint identification are couched in terms of the faces of these polyhedra the main result employs a nondegeneracy condition due to dunn 7 and the linear independence condition to obtain a characterization of those algorithms that identify the optimal active constraints in a finite number of iterations the role of the linear independence condition is carefully examined and it is argued that it is required within the context of a first order theory of constraint identification in conclusion the characterization theorem is applied to the wilson han powell sequential quadratic programming algorithm j optim theory appl 22 1977 pp 297 309 proceedin

chow groups of projective varieties of very small degree see 12 5 and the references given there these facts together with various conjectures on the cohomology and chow groups of algebraic varieties suggest that the chow groups of x might satisfy chl x q chl pk q q for l 1 compare with remark 5 6 and corollary 5 7 this is explicitly formulated by v srinivas and k paranjape in 16 conjecture 1 8 the chain of reasoning goes roughly as follows suppose x is smooth one expects a good filtration 0 f j 1 f j f 0 ch x x q whose graded pieces f f l 1 are controlled by h2j l x x see 10 according to grothendieck s generalized conjecture 8 the groups h x should be generated by the image under the gysin morphism of the homology of a codimension subset together with the classes coming from p applying this to the diagonal in x x should then force the triviality of the chow groups in the desired range for zero cycles the conjecture follows from roitman s theorem see 17 and 18

nonlinear programming algorithms using trust regions and augmented lagrangians with nonmonotone penalty parameters the strategy for obtaining global convergence is based on the trust region approach the merit function is a type of augmented lagrangian a new updating scheme is introduced for the penalty parameter by means of which monotone increase is not necessary global convergence results are proved and numerical experiments are presented

a nonmonotone trust region algorithm with nonmonotone penalty parameters for constrained optimization in this paper we present a nonmonotone trust region algorithm with nonmonotone penalty parameters for the solution of optimization problems with nonlinear equality constraints and bound constraints the proposed algorithm combines an sqp approach with a trust region strategy to globalize the process each step is obtained through the computation of a normal step to reduce infeasibility and a tangential step to decrease some merit function the algorithm makes use of an augmented lagrangian function as merit function and allows the value of this merit function and the penalty parameter involved in it to decrease non monotonically the global convergence theory for the proposed algorithm is developed without regularity assumption and shows that any limit point of the sequence generated by the algorithm is a stationary point while at least one limit point under the suitable assumptions is a substationary point and a stationary point if it is feasible some preliminary numerical experiments are also reported

subdifferential regularities of perturbed distance functions outside the target set in banach spaces abstract this paper is devoted to study the frechet and proximal regularities at points outside the target set of perturbed distance functions d s j determined by a closed subset s and a lipschitz function j also we provide some important results on the frechet proximal and clarke subdifferentials of d s j at those points in banach spaces

canonical euler splitting method for nonlinear composite stiff evolution equations in this paper a new splitting method called canonical euler splitting method ces is constructed and studied which can be used for the efficient numerical solution of general nonlinear composite stiff problems in evolution equations of various type such as ordinary differential equations odes semi discrete unsteady partial differential equations pdes and ordinary or partial volterra functional differential equations vfdes and can significantly improve the computing speed on the basis of ensuring the computing quality stability consistency and convergence theories of this method are established a series of numerical experiments are given which check the efficiency of ces method and confirm our theoretical results

on the convergence of a new trust region algorithm in this paper we present a new trust region algorithm for general nonlinear constrained optimization problems the algorithm is based on the l infty exact penalty function under very mild conditions global convergence results for the algorithm are given local convergence properties are also studied it is shown that the penalty parameter generated by the algorithm will be eventually not less than the l 1 norm of the lagrange multipliers at the accumulation point it is proved that the method is equivalent to the sequential quadratic programming method for all large k hence superlinearly convergent results of the sqp method can be applied numerical results are also reported

examples of smash nilpotent cycles on rationally connected varieties abstract voevodsky has conjectured that numerical and smash equivalence coincide on a smooth projective variety we prove this conjecture holds for uniruled 3 folds 4 folds whose mrcc quotient has dimension 2 and for smooth complete intersections with very small degree

finite element approximation of the transport of reactive solutes in porous media part 1 error estimates for nonequilibrium adsorption processes in this paper we analyze a fully practical piecewise linear finite element approximation involving numerical integration backward euler time discretization and possibly regularization of the following degenerate parabolic system arising in a model of reactive solute transport in porous media find u x t v x t such that begin eqnarray partial t u partial t v delta u f quad mbox in omega times 0 t qquad u 0 quad mbox on partial omega times 0 t partial tv k varphi u v quad mbox in omega times 0 t u cdot 0 g 1 cdot quad v cdot 0 g 2 cdot quad mbox in omega subset real d quad 1 le d le 3 end eqnarray for given data k in real f g 1 g 2 and a monotonically increasing varphi in c 0 real cap c 1 infty 0 cup 0 infty satisfying varphi 0 0 which is only locally holder continuous with exponent p in 0 1 at the origin e g varphi s equiv s p this lack of lipschitz continuity at the origin limits the regularity of the unique solution u v and leads to difficulties in the finite element error analysis

a sequential quadratic programming method for potentially infeasible mathematical programs abstract the paper describes a modification to the wilson han powell sequential quadratic programming technique that is applicable to potentially infeasible nonlinear programs the method is designed to locate stationary points of a nonlinear program in a generalized sense definition 2 8 these stationary points include the familiar kuhn tucker and fritz john points but also include what we call external and strong external stationary points the external and strong external stationary points are not feasible thus the problem may be infeasible and yet have stationary points loosely speaking an external stationary point is one that satisfies a certain first order necessary optimality condition for being as close to feasibility as possible the proposed technique is similar to those described by j v burke and s p han a modified sequential quadratic programming method manuscript and m sahba j optim theory appl 52 1987 291 309 however it is shown to possess substantially enhanced stability properties the global convergence properties of the method are described along with some continuity results for the quadratic programming subproblems

a simple feasible sqp algorithm for inequality constrained optimization in this paper an sqp method generating feasible iterates is presented to solve the nonlinear inequality constrained optimization problems a new modified method which ensures the global and superlinear convergence is proposed by solving systems of linear equation instead of qp subproblems and linear squares problems here the search direction is a suitable combination of a descent direction a feasible direction and a second order revised direction the theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions

a precise numerical scheme for contaminant transport in dual well flow 1 a precise numerical method is developed for the simulation of contaminant transport in dual well flow our main motivation is the determination of model parameters by means of dual well tests the method presented here guarantees a very low level of numerical dispersion we have applied a bipolar transformation to the transport equation so that the convective term is parallel to one of the axes in the time stepping we split the transport and diffusion parts the transport part is semianalytically solved thanks to the bipolar transformation via a multiple riemann problem and the diffusion part is solved using a finite volume method examples are provided to show that the method is suitable for parameter identification

solution of convection diffusion problems with nonequilibrium adsorption in this paper an efficient method for solving contaminant transport problem with diffusion and adsorption in nonequilibrium mode is introduced the method is based on operator splitting approach where the solution of the transport problem is found in an analytical form and the diffusion problem is solved by finite volume method finally the system corresponding to nonequilibrium adsorption problem is transformed to one integral equation which is solved numerically using time discretization some numerical aspects of the problem are discussed and various results of numerical experiments are shown as well as a comparison to precise semi analytical solution for special cases

epi convergent smoothing with applications to convex composite functions smoothing methods have become part of the standard tool set for the study and solution of nondifferentiable and constrained optimization problems as well as a range of other variational and equilibrium problems in this note we synthesize and extend recent results due to beck and teboulle on infimal convolution smoothing for convex functions with those of x chen on gradient consistency for nonconvex functions we use epi convergence techniques to define a notion of epi smoothing that allows us to tap into the rich variational structure of the subdifferential calculus for nonsmooth nonconvex and nonfinite valued functions as an illustration of the versatility and range of epi smoothing techniques the results are applied to the general constrained optimization for which nonlinear programming is a special case

decent intersection and tor rigidity for modules over local hypersurfaces first published in transactions of the american mathematical society in 2013 published by the american mathematical society also available electronically from http www ams org journals tran 2013 365 06 s0002 9947 2012 05574 7 home html

an augmented lagrangian function with improved exactness properties in this paper we introduce a new exact augmented lagrangian function for the solution of general nonlinear programming problems for this lagrangian function a complete equivalence between its unconstrained minimization on an open set and the solution of the original constrained problem can be established under mild assumptions and without requiring the boundedness of the feasible set of the constrained problem moreover we describe an unconstrained algorithmic model which is globally convergent toward kkt pairs of the original constrained problem the algorithmic model can be endowed with a superlinear rate of convergence by a proper choice of the search direction in the unconstrained minimization without requiring strict complementarity

second order necessary and sufficient conditions for convex composite ndo in convex composite ndo one studies the problem of minimizing functions of the formf h f whereh m is a finite valued convex function andf n m is continuously differentiable this problem model has a wide range of application in mathematical programming since many important problem classes can be cast within its framework e g convex inclusions minimax problems and penalty methods for constrained optimization in the present work we extend the second order theory developed by a d ioffe in 11 12 13 for the case in whichh is sublinear to arbitrary finite valued convex functionsh moreover a discussion of the second order regularity conditions is given that illuminates their essentially geometric nature

on using the elastic mode in nonlinear programming approaches to mathematical programs with complementarity constraints we investigate the possibility of solving mathematical programs with complementarity constraints mpccs using algorithms and procedures of smooth nonlinear programming although mpccs do not satisfy a constraint qualification we establish sufficient conditions for their lagrange multiplier set to be nonempty mpccs that have nonempty lagrange multiplier sets and satisfy the quadratic growth condition can be approached by the elastic mode with a bounded penalty parameter in this context the elastic mode transforms mpcc into a nonlinear program with additional variables that has an isolated stationary point and local minimum at the solution of the original problem which in turn makes it approachable by sequential quadratic programming sqp algorithms one such algorithm is shown to achieve local linear convergence once the problem is relaxed under stronger conditions we also prove superlinear convergence to the solution of an mpcc using an adaptive elastic mode approach for an sqp algorithm recently analyzed in an mpcc context in r fletcher s leyffer s sholtes and d ralph local convergence of sqp methods for mathematical programs with equilibrium constraints tech report na 210 university of dundee dundee uk 2002 our assumptions are more general since we do not use a critical assumption from that reference in addition we show that the elastic parameter update rule will not interfere locally with the superlinear convergence once the penalty parameter is appropriately chosen

an inequality constrained nonlinear kalman bucy smoother by interior point likelihood maximization kalman bucy smoothers are often used to estimate the state variables as a function of time in a system with stochastic dynamics and measurement noise this is accomplished using an algorithm for which the number of numerical operations grows linearly with the number of time points all of the randomness in the model is assumed to be gaussian including other available information for example a bound on one of the state variables is non trivial because it does not fit into the standard kalman bucy smoother algorithm in this paper we present an interior point method that maximizes the likelihood with respect to the sequence of state vectors satisfying inequality constraints the method obtains the same decomposition that is normally obtained for the unconstrained kalman bucy smoother hence the resulting number of operations grows linearly with the number of time points we present two algorithms the first is for the affine case and the second is for the nonlinear case neither algorithm requires the optimization to start at a feasible sequence of state vector values both the unconstrained affine and unconstrained nonlinear kalman bucy smoother are special cases of the class of problems that can be handled by these algorithms

solution of contaminant transport with equilibrium and non equilibrium adsorption abstract in this paper we present a numerical approximation scheme for the solution of contaminant transport problems with diffusion and adsorption in equilibrium and non equilibrium mode the method is based on time stepping and operator splitting the non linear transport is solved semi analytically via the multiple riemann problem the non linear diffusion by a finite volume method and by newton s type of linearisation and finally the reaction part incorporating the non equilibrium adsorption is transformed to an integral equation which is solved numerically using time discretization various results of numerical experiments are shown and the method is applied to the practical dual well problem

the nonlinear programming method of wilson han and powell with an augmented lagrangian type line search function the paper represents an outcome of an extensive comparative study of nonlinear optimization algorithms this study indicates that quadratic approximation methods which are characterized by solving a sequence of quadratic subproblems recursively belong to the most efficient and reliable nonlinear programming algorithms available at present the purpose of this paper is to analyse the theoretical convergence properties and to investigate the numerical performance in more detail in part 1 the exactl 1 penalty function of han and powell is replaced by a differentiable augmented lagrange function for the line search computation to the able to prove the global convergence and to show that the steplength one is chosen in the neighbourhood of a solution in part 2 the quadratic subproblem is exchanged by a linear least squares problem to improve the efficiency and to test the dependence of the performance from different solution methods for the quadratic or least squares subproblems

action of correspondences on filtrations on cohomology and 0 cycles of abelian varieties we prove that given a symmetrically distinguished correspondence of a suitable complex abelian variety which includes any abelian variety of dimension at most 5 powers of complex elliptic curves etc that vanishes as a morphism on a certain quotient of its middle singular cohomology then it vanishes as a morphism on the deepest part of a particular filtration on the chow group of 0 cycles of the abelian variety as a consequence we prove that an automorphism of such an abelian variety that acts as the identity on a certain quotient of its middle singular cohomology acts as the identity on the deepest part of this filtration on the chow group of 0 cycles of the abelian variety as an application we prove that for the generalized kummer variety associated to a complex abelian surface and the automorphism induced from a symplectic automorphism of the complex abelian surface the automorphism of the generalized kummer variety acts as the identity on a certain subgroup of its chow group of 0 cycles

a sequential quadratic optimization algorithm with rapid infeasibility detection we present a sequential quadratic optimization sqo algorithm for nonlinear constrained optimization the method attains all of the strong global and fast local convergence guarantees of classical sqo methods but has the important additional feature that fast local convergence is guaranteed when the algorithm is employed to solve infeasible instances a two phase strategy carefully constructed parameter updates and a line search are employed to promote such convergence the first phase subproblem determines the reduction that can be obtained in a local model of an infeasibility measure when the objective function is ignored the second phase subproblem then seeks to minimize a local model of the objective while ensuring that the resulting search direction attains a reduction in the local model of the infeasibility measure that is proportional to that attained in the first phase the subproblem formulations and parameter updates ensure that near an optimal solution the algorithm reduces to a classica

a variant of sqp method for inequality constrained optimization and its global convergence in this paper a variant of sqp method for solving inequality constrained optimization is presented this method uses a modified qp subproblem to generate a descent direction as each iteration and can overcome the possible difficulties that the qp subproblem of the standard sqp method is inconsistency furthermore the method can start with an infeasible initial point under mild conditions we prove that the algorithm either terminates as kkt point within finite steps or generates an infinite sequence whose accumulation point is a kkt point or satisfies certain first order necessary condition finally preliminary numerical results are reported

a feasible sqp method for nonlinear programming in this paper a new sqp algorithm is presented to solve the general nonlinear programs with mixed equality and inequality constraints quoted from p spellucci see 9 this method maybe be named sequential equality constrained quadratic programming secqp algorithm per single iteration based on an active set strategy see 9 this secqp algorithm requires only to solve equality constrained quadratic programming subproblems or system of linear equations the theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions

bloch s conjecture for catanese and barlow surfaces catanese surfaces are regular surfaces of general type with pg 0 they specialize to double covers of barlow surfaces we prove that the ch0 group of a catanese surface is equal to z which implies the same result for the barlow surfaces

a global convergence theory for dennis el alem and maciel s class of trust region algorithms for constrained optimization without assuming regularity this work presents a convergence theory for dennis el alem and maciel s class of trust region based algorithms for solving the smooth nonlinear programming problem with equality constraints the results are proved under very mild conditions on the quasi normal and tangential components of the trial steps the lagrange multiplier estimates and the hessian estimates are assumed to be bounded no regularity assumption is made in particular linear independence of the gradients of the constraints is not assumed the theory proves global convergence for the class in particular it shows that a subsequence of the iteration sequence satisfies one of four types of mayer bliss stationary conditions in the limit

a robust algorithm for optimization with general equality and inequality constraints an algorithm for general nonlinearly constrained optimization is presented which solves an unconstrained piecewise quadratic subproblem and a quadratic programming subproblem at each iterate the algorithm is robust since it can circumvent the difficulties associated with the possible inconsistency of qp subproblem of the original sqp method moreover the algorithm can converge to a point which satisfies a certain first order necessary optimality condition even when the original problem is itself infeasible which is a feature of burke and han s methods math programming 43 1989 pp 277 303 unlike burke and han s methods our algorithm does not introduce additional bound constraints the algorithm solves the same subproblems as the han powell sqp algorithm at feasible points of the original problem under certain assumptions it is shown that the algorithm coincides with the han powell method when the iterates are sufficiently close to the solution some global convergence results are proved and locally superlinear convergence results are also obtained preliminary numerical results are reported

on the action of symplectic automorphisms on the mathrm ch _0 groups of some hyper kahler fourfolds we prove that for any polarized symplectic automorphism of the fano variety of lines of a smooth cubic fourfold equipped with the plucker polarization the induced action on the chow group of 0 cycles is identity as predicted by bloch beilinson conjecture we also prove the same result for the chow group of homologically trivial 2 cycles up to torsion

chow groups are finite dimensional in some sense when s is a surface with pg s 0 mumford proved that its chow group a s is not finite dimensional in some sense in this paper we propose another definition of finite dimensionality for the chow groups using this new definition at least the chow group of some surface s with pg s 0 for example the product of two curves becomes finite dimensional the finite dimensionality of the chow groups follows from the finite dimensionality of the chow motives it turns out that the finite dimensionality of the chow motives is a very strong property for example we can prove bloch s conjecture representability of the chow groups of surfaces with pg s 0 under the assumption that the chow motive of s is finite dimensional

parameter estimation in convection dominated nonlinear convection diffusion problems by the relaxation method and the adjoint equation the development of numerical methods for strongly nonlinear convection diffusion problems with dominant convection is an ongoing topic in numerical analysis for inverse problems in this setting there is a need of fast and accurate solvers here we present operator splitting with a riemann solver for the convective part and a relaxation method for the diffusive part as a means to achieve this goal combined with the adjoint equation method this allows us to solve inverse problems within reasonable time frames and with modest computing power as an example the dual well experiment is considered and the adjoint method is compared with a conjugate gradient algorithm and a levenberg marquardt type of iteration method