inseparable local uniformization abstract it is known since the works of zariski in the early 40s that desingularization of varieties along valuations called local uniformization of valuations can be considered as the local part of the desingularization problem it is still an open problem if local uniformization exists in positive characteristic and dimension larger than three in this paper we prove that zariski local uniformization of algebraic varieties is always possible after a purely inseparable extension of the field of rational functions and therefore any valuation can be uniformized by a purely inseparable alteration

new results on a continuously differentiable exact penalty function the main motivation of this paper is to weaken the conditions that imply the correspondence between the solution of a constrained problem and the unconstrained minimization of a continuously differentiable function in particular a new continuously differentiable exact penalty function is proposed for the solution of nonlinear programming problems under mild assumptions a complete equivalence can be established between the solution of the original constrained problem and the unconstrained minimization of this penalty function on a perturbation of the feasible set this new penalty function and its exactness properties allow us to define globally and superlinearly convergent algorithms to solve nonlinear programming problems as an example a newton type algorithm is described which converges locally in one iteration in case of quadratic programming problems

a continuously differentiable exact penalty function for nonlinear programming problems with inequality constraints in this paper it is shown that given a nonlinear programming problem with inequality constraints it is possible to construct a continuously differentiable exact penalty function whose global or local unconstrained minimizers correspond to global or local solutions of the constrained problem

the model theory of separably tame valued fields a henselian valued field k is called separably tame if its separable algebraic closure ksep is a tame extension that is the ramification field of the normal extension ksep k is separable algebraically closed every separable algebraically maximal kaplansky field is a separably tame field but not conversely in this paper we prove ax kochen ershov principles for separably tame fields this leads to model completeness and completeness results relative to the value group and residue field as the maximal immediate extensions of separably tame fields are in general not unique the proofs have to use much deeper valuation theoretical results than those for other classes of valued fields which have already been shown to satisfy ax kochen ershov principles our approach also yields alternate proofs of known results for separably closed valued fields

iteration complexity of first order augmented lagrangian methods for convex programming this paper considers a special class of convex programming cp problems whose feasible regions consist of a simple compact convex set intersected with an affine manifold we present first order methods for this class of problems based on an inexact version of the classical augmented lagrangian al approach where the subproblems are approximately solved by means of nesterov s optimal method we then establish a bound on the total number of nesterov s optimal iterations i e the inner iterations performed throughout the entire inexact al method to obtain a near primal dual optimal solution we also present variants with possibly better iteration complexity bounds than the original inexact al method which consist of applying the original approach directly to a perturbed problem obtained by adding a strongly convex component to the objective function of the cp problem

differentiable exact penalty functions for nonlinear second order cone programs we propose a method for solving nonlinear second order cone programs socps based on a continuously differentiable exact penalty function the construction of the penalty function is given by incorporating a multipliers estimate in the augmented lagrangian for socps under the nondegeneracy assumption and the strong second order sufficient condition we show that a generalized newton method has global and superlinear convergence we also present some preliminary numerical experiments

on an exact penalty function method for nonlinear mixed discrete programming problems and its applications in search engine advertising problems in this paper we study a new exact and smooth penalty function for the nonlinear mixed discrete programming problem by augumenting only one variable no matter how many constraints through the smooth and exact penalty function we can transform the nonlinear mixed discrete programming problem into an unconstrained optimization model we demonstrate that under mild conditions when the penalty parameter is sufficiently large optimizers of this penalty function are precisely the optimizers of the nonlinear mixed discrete programming problem alternatively under some mild assumptions the local exactness property is also presented the numerical results demonstrate that the new penalty function is an effective and promising approach as important applications we solve an increasingly popular search engine advertising problem via the new proposed penalty function

algebraic independence of elements in immediate extensions of valued fields abstract refining a constructive combinatorial method due to maclane and schilling we give several criteria for a valued field that guarantee that all of its maximal immediate extensions have infinite transcendence degree if the value group of the field has countable cofinality then these criteria give the same information for the completions of the field the criteria have applications to the classification of valuations on rational function fields we also apply the criteria to the question of which extensions of a maximal valued field algebraic or of finite transcendence degree are again maximal in the case of valued fields of infinite p degree we obtain the worst possible examples of nonuniqueness of maximal immediate extensions fields which admit an algebraic maximal immediate extension as well as one of infinite transcendence degree

managing diversity in regression ensembles ensembles are a widely used and effective technique in machine learning their success is commonly attributed to the degree of disagreement or diversity within the ensemble for ensembles where the individual estimators output crisp class labels this diversity is not well understood and remains an open research issue for ensembles of regression estimators the diversity can be exactly formulated in terms of the covariance between individual estimator outputs and the optimum level is expressed in terms of a bias variance covariance trade off despite this most approaches to learning ensembles use heuristics to encourage the right degree of diversity in this work we show how to explicitly control diversity through the error function the first contribution of this paper is to show that by taking the combination mechanism for the ensemble into account we can derive an error function for each individual that balances ensemble diversity with individual accuracy we show the relationship between this error function and an existing algorithm called negative correlation learning which uses a heuristic penalty term added to the mean squared error function it is demonstrated that these methods control the bias variance covariance trade off systematically and can be utilised with any estimator capable of minimising a quadratic error function for example mlps or rbf networks as a second contribution we derive a strict upper bound on the coefficient of the penalty term which holds for any estimator that can be cast in a generalised linear regression framework with mild assumptions on the basis functions finally we present the results of an empirical study showing significant improvements over simple ensemble learning and finding that this technique is competitive with a variety of methods including boosting bagging mixtures of experts and gaussian processes on a number of tasks

a robust sequential quadratic programming method the sequential quadratic programming method developed by wilson han and powell may fail if the quadratic programming subproblems become infeasible or if the associated sequence of search directions is unbounded this paper considers techniques which circumvent these difficulties by modifying the structure of the constraint region in the quadratic programming subproblems furthermore questions concerning the occurrence of an unbounded sequence of multipliers and problem feasibility are also addressed

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

valuations on rational function fields that are invariant under permutation of the variables abstract we study and characterize the class of valuations on rational functions fields that are invariant under permutation of the variables and can be extended to valuations with the same property whenever a finite number of new variables is adjoined the gaus valuation is in this class which constitutes a natural generalization of the concept of gaus valuation further we apply our characterization to show that the most common ad hoc generalization of the gaus valuation is also in this class

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

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

exact penalty functions in constrained optimization in this paper formal definitions of exactness for penalty functions are introduced and sufficient conditions for a penalty function to be exact according to these definitions are stated thus providing a unified framework for the study of both nondifferentiable and continuously differentiable penalty functions in this framework the best known classes of exact penalty functions are analyzed and new results are established concerning the correspondence between the solutions of the constrained problem and the unconstrained minimizers of the penalty functions

elimination of ramification i the generalized stability theorem we prove a general version of the stability theorem if k is a valued field such that the ramification theoretical defect is trivial for all of its finite extensions and if f k is a finitely generated transcendental extension of valued fields for which equality holds in the abhyankar inequality then the defect is also trivial for all finite extensions of f this theorem is applied to eliminate ramification in such valued function fields it has applications to local uniformization and to the model theory of valued fields in positive characteristic

the global convergence of augmented lagrangian methods based on ncp function in constrained nonconvex optimization abstract in this paper we present the global convergence properties of the primal dual method using a class of augmented lagrangian functions based on ncp function for inequality constrained nonconvex optimization problems we construct four modified augmented lagrangian methods based on different algorithmic strategies we show that the convergence to a kkt point or a degenerate point of the original problem can be ensured without requiring the boundedness condition of the multiplier sequence

serial and parallel computation of karush kuhn tucker points via nonsmooth equations in this paper a robust iterative algorithm is presented for computing karush kuhn tucker kkt points of nonlinear programs this algorithm is a variation of the ne sqp method for solving the nonlinear complementarily problem it makes use of a merit function that combines the original objective function of the nonlinear program with a residual function of the kkt conditions formulated as a system of nonsmooth equations global convergence and a q quadratic rate of convergence of the algorithm are established under some standard constraint qualifications in nonlinear programming theory but without the strict complementarily condition parallel implementations of the algorithm are discussed

counting the number of distinct distances of elements in valued field extensions abstract the defect of valued field extensions is a major obstacle in open problems in resolution of singularities and in the model theory of valued fields whenever positive characteristic is involved we continue the detailed study of defect extensions through the tool of distances which measure how well an element in an immediate extension can be approximated by elements from the base field we show that in several situations the number of essentially distinct distances in fixed extensions or even just over a fixed base field is finite and we compute upper bounds we apply this to the special case of valued functions fields over perfect base fields in particular this provides important information used in forthcoming research on the ramification theory of two dimensional valued function fields

every place admits local uniformization in a finite extension of the function field we prove that every place p of an algebraic function field f k of arbitrary characteristic admits local uniformization in a finite extension f of f we show that f f can be chosen to be galois after a finite purely inseparable extension of the ground field k instead of being galois the extension can also be chosen such that the induced extension fp fp of the residue fields is purely inseparable and the value group of f only gets divided by the residue characteristic if f lies in the completion of an abhyankar place then no extension of f is needed our proofs are based solely on valuation theoretical theorems which are of particular importance in positive characteristic they are also applicable when working over a subring r k and yield similar results if r is regular and of dimension smaller than 3

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs