existence of solutions for first order ordinary differential equations with nonlinear boundary conditions we present an existence theorem for nonlinear ordinary differential equations of first order with nonlinear boundary conditions the result includes for instance the initial value problem the final value problem and the antiperiodic boundary value problem the main novelty of the method lies in that it unifies different techniques for initial or boundary conditions

stationarity and superlinear convergence of an algorithm for univariate locally lipschitz constrained minimization this paper introduces an algorithm for minimizing a single variable locally lipschitz function subject to a like function being nonpositive the method combines polyhedral and quadratic approximation a new type of penalty technique and a safeguard in such a way as to give convergence to a stationary point the convergence is shown to be superlinear under somewhat stronger assumptions that allow both nonsmooth and nonconvex cases the algorithm can be an effective subroutine for solving line search subproblems called for by multivariable optimization algorithms

restricted center problems under polyhedral gauges abstract given a finite set ex ex 1 ex 2 ex m in the plane and a forbidden region r we want to find a point x r such that max m 1 m w m m x ex m is minimized this is a variant of the well known continuous center problem where we measure the distance with polyhedral gauges the unit ball of a polyhedral gauge may be any convex polyhedron containing the origin in its interior this large class of distance functions allows very general practical settings such as asymmetry to be modeled each ex m is allowed to have its own gauge m and the forbidden region r enables us to include negative information which means defining the infeasible region explicitly instead of the feasible region in the model efficient algorithms and structural properties for this non convex optimization problem based on combinatorial and geometrical methods are presented a classification scheme for location problems is also introduced

ordinary differential equations with nonlinear boundary conditions of antiperiodic type abstract the quasilinearization method is successfully applied to differential problems with nonlinear boundary conditions of antiperiodic type given are sufficient conditions under which the monotone iterations converge quadratically to a unique solution of our problem the advantage of this approach lies in the fact that the approximate solutions are obtained iteratively as solutions of the above mentioned iterations

first order impulsive ordinary differential equations with anti periodic and nonlinear boundary conditions the monotone iterative technique is a powerful method that have been used to approximate the extremal solutions of several problems 1 2 on the other hand impulsive differential equations are a basic tool to study some problems of biology medicine engineering and physics 3 in this paper we deal with the following nonlinear boundary value problem for first order differential equation with impulses at fixed points

a bracketing technique to ensure desirable convergence in univariate minimization this paper gives a general safeguarded bracketing technique for minimizing a function of a single variable in certain cases the technique guarantees convergence to a stationary point and when combined with sequential polynomial and or polyhedral fitting algorithms preserves rapid convergence each bracket has an interior point whose function value does not exceed those of the two bracket endpoints the safeguarding technique consists of replacing the fitting algorithm s iterate candidate by a close point whose distance from the three bracket points exceeds a positive multiple of the square of the bracket length it is shown that a given safeguarded quadratic fitting algorithm converges in a certain better than linear manner with respect to the bracket endpoints for a strongly convex twice continuously differentiable function

a algorithm for convex minimization for convex minimization we introduce an algorithm based on space decomposition the method uses a bundle subroutine to generate a sequence of approximate proximal points when a primal dual track leading to a solution and zero subgradient pair exists these points approximate the primal track points and give the algorithm s or corrector steps the subroutine also approximates dual track points that are gradients needed for the method s newton predictor steps with the inclusion of a simple line search the resulting algorithm is proved to be globally convergent the convergence is superlinear if the primal dual track points and the objective s hessian are approximated well enough

inference for the binomial n parameter a hierarchical bayes approach summary a hierarchical bayes approach to the problem of estimating n in the binomial distribution is presented this provides a simple and flexible way of specifying prior information and also allows a convenient representation of vague prior knowledge it yields solutions to the problems of interval estimation prediction and decision making as well as that of point estimation the bayes estimator compares favourably with the best previously proposed point estimators in the literature unknown parameters n and 0 most of the literature about statistical analysis of this model has focused on point estimation of n while interval estimation prediction and decision making have been little considered see 2 i adopt a hierarchical bayes approach this provides a simple way of specifying prior information and also allows a convenient representation of vague prior knowledge using limiting improper prior forms it leads to solutions of the problems of interval estimation prediction and decision making as well as that of point estimation a difficulty with bayesian analysis of this problem has been the absence of a sufficiently flexible and tractable family of prior distributions mainly due to the fact that n is an integer the present approach gets around this by first assuming that n has a poisson distribution the resulting hyperparameters are then continuous valued and one may use existing results about conjugate and vague priors in better understood settings

a generalization of the method of upper and lower solutions for discontinuous first order problems with nonlinear boundary conditions in this paper we prove the existence of extremal solutions for a discontinuous bvp between a lower and an upper solution which may be discontinuous in a finite set of points furthermore we present a monotone method with which we can explicitly construct a pair of sequences that converge to the extremal solutions despite the discontinuities of the right hand side of the equation

existence and approximation of solutions for first order discontinuous difference equations with nonlinear global conditions in the presence of lower and upper solutions abstract this paper is devoted to the study of the existence of solutions of first order difference equations verifying nonlinear conditions that involve the global behavior of the solution we prove that the existence of lower and upper solutions warrants the existence of such solutions lying in the sector formed by the mentioned functions we also can prove that some classical results for differential equations are not true in general for this case

the monotone method for first order problems with linear and nonlinear boundary conditions in this paper we develop the monotone method for the first order problem u t f t u t for a e t a b when f is a caratheodory function and u w 1 1 a b we consider the nonlinear boundary conditions l u a u b 0 with l c r 2 r nondecreasing in x or nonincreasing in y and the linear boundary conditions a 0u 0 b 0u t l 0 with a 0 b 0 and l 0 r we prove the existence of solutions and the validity of the monotone method if there exists a lower solution a and an upper solution b with either a b for the linear conditions we obtain eight new concepts of lower and upper solutions which generalize previous known cases

on superlinear convergence in univariate nonsmooth minimization this note demonstrates a new result on superlinear convergence in nonsmooth univariate minimization it also gives other concepts of rapid convergence for minimization of functions that may have discontinuous derivatives

global and superlinear convergence of an algorithm for one dimensional minimization of convex functions this paper studies an algorithm for minimizing a convex function based upon a combination of polyhedral and quadratic approximation the method was given earlier but without a good specification for updating the algorithm s curvature matrix here for the case of onedimensional minimization we provide a specification that insures convergence even in cases where the curvature scalar tends to zero or infinity under mild additional assumptions we show that the convergence is superlinear

admissible estimation of the binomial parameter n suppose that x has a binomial distribution b n p with known p in 0 1 and unknown n in 1 2 cdots a natural estimator for n is given by t 0 1 t x x p x 1 2 cdots this estimator is shown to be inadmissible under quadratic loss it is shown that modifying t 0 to t 0 1 p p ln p results in an admissible estimator for p geq frac 1 2 it is further shown that this is the only admissible modification of t 0 a partial result is also obtained for p frac 1 2

a quasi second order proximal bundle algorithm this paper introduces an algorithm for convex minimization which includes quasi newton updates within a proximal point algorithm that depends on a preconditioned bundle subalgorithm the method uses the hessian of a certain outer function which depends on the jacobian of a proximal point mapping which in turn depends on the preconditioner matrix and on a lagrangian hessian relative to a certain tangent space convergence is proved under boundedness assumptions on the preconditioner sequence

existence results for discontinuous functional differential systems in this paper we study solvability of first order discontinuous functional differential systems equipped with discontinuous functional initial conditions a concrete example is presented and solved to illustrate the obtained results

a comparison of n estimators for the binomial distribution abstract estimating the number n of trials given a sequence of independent success counts obtained by replicating the n trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution both the method of moments and the maximum likelihood estimators of n are considered when p is unknown and small while n is large both estimators become highly unstable stabilized versions of these estimators are proposed and their performance is described in terms of results obtained by simulation

a discontinuous functional differential equation abstract in this paper we give a sufficient condition for the existence of maximal and minimal solutions to a discontinuous functional differential equation x t f t x t x x 0 0 we apply the result to establish an existence theorem for the darboux problem for a partial differential equation

upper and lower solutions method for first order impulsive differential inclusions with nonlinear boundary conditions abstract in this paper a fixed point theorem for condensing multivalued maps due to martelli combined with the concept of upper and lower solutions is used to investigate the existence of solutions for first order impulsive differential inclusions with nonlinear boundary conditions