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In the paper, a new trust region algorithm is given for nonlinear inequality constrained optimization problems. Motivated by a dual problem introduced by Han and Mangasarian [Han, S. P., Mangasarian, O. L. (1983). A dual differentiable exact penalty function. Math. Programming 25:293-306], which is a nonnegatively constrained maximization problem, we construct a trust region algorithm for solving the dual problem. At each iteration, we only need to minimize a quadratic subproblem with simple bound constraints. Under the condition that the iterate sequence generated by the algorithm is contained in some bounded closed set, any accumulation point of the sequence is a Karush- Kuhn-Tucker point of the original problem. [ABSTRACT FROM AUTHOR]

Kolodko and Schoenmakers (2006) and Bender and Schoenmakers (2006) introduced a policy iteration that allows the achievement of a tight lower approximations of the price for early exercise options via a nested Monte Carlo simulation in a Markovian setting. In this paper we enhance the algorithm by a scenario selection method. It is demonstrated by numerical examples that the scenario selection can significantly reduce the number of inner simulations actually performed, and thus can greatly speed up the method (by up to a factor of 15 in some examples). Moreover, it is shown that the modified algorithm retains the desirable properties of the original, such as the monotone improvement property, termination after a finite number of iteration steps, and numerical stability. [ABSTRACT FROM AUTHOR]

The aim of our paper is to provide a new class of five-phase anti-lock brake algorithms (that use wheel deceleration logic-based switching) and a simple mathematical background that explains their behavior. First, we completely characterize the conditions required for our algorithm to work. Next, we explain how to compute analytically an approximation of the Poincaré map of the system (without using numerical integration) and show how to calibrate the algorithm’s parameters to obtain the most efficient limit cycle. [ABSTRACT FROM AUTHOR]

The p -centre problem is to locate p facilities on a network so as to minimize the largest distance from a demand point to its nearest facility. The problem is NP-complete for an arbitrary network. In this paper, genetic algorithms (GAs) to solve this problem are developed via two different representations. The nodes are taken as weighted, and the demand points are assumed to coincide with the nodes. Computational results obtained from the proposed GAs for different network sizes and different values of p are presented and compared for two different representations. [ABSTRACT FROM AUTHOR]

This paper inductively investigates an inverse problem for difference boundary value problems with boundary conditions that depend quadratically on the eigenparameter. In particular, given the eigenvalues and the weights, we provide an algorithm to uniquely reconstruct the potential. [ABSTRACT FROM AUTHOR]

The Steiner Problem in graphs is the problem of finding a set of edges (arcs) with minimum total weight which connects a given set of nodes in an edge-weighted graph (directed or undirected). This paper develops models for the directed Steiner tree problem on graphs. New and old models are examined in terms of their amenability to solution schemes based on Lagrangean relaxation. As a result, three alogrithms are presented and their performance compared on a number of problems originally tested by Beasley (1984, 1987) in the case of undirected graphs. [ABSTRACT FROM AUTHOR]

A multi resolution transform corresponding to interpolatory techniques is used for fast application of second order Taylor's approximations. In designing this algorithm we apply data compression to the linear and the bilinear forms that appear on the approximation. Analysis of the error is performed. Finally, some numerical results are presented. [ABSTRACT FROM AUTHOR]

While in Part I (see [1]) and Part II (see [2]) of this three-part exposition we focused attention on non-dissipative symplectic-momentum conserving designs of time operators for applicability to nonlinear dynamics, here in Part III of this exposition we demonstrate how to further advance the theoretical developments and introduce controllable numerical dissipation via a novel time weighted residual approach we have previously described. The unique aspects of the algorithmic designs are such that when the numerical dissipative features are turned off, the resulting time operators readily recover the original designs of algorithms that are inherently symplectic-momentum conserving (we defer to those that are energy-momentum conserving elsewhere [3, 4]). The focus of the current work is on the theoretical developments of the new formulation termed the displacement based normalized time weighted residual approach for nonlinear dynamics applications. In particular, we provide extensions of the well—known Generalized Single Solve Single Step (GSSSS) framework, which comprises two distinct classifications, namely constrained U and V algorithmic architectures, and was originally developed for solving linear dynamic problems. Starting with the generalization of the classical time weighted residual approach, the GSSSS framework that was previously developed encompasses the general class of LMS methods represented by the single field form of the second order ordinary differential equations in time involving a single solve, and also covers most of the developments to date in the literature, including providing new avenues towards optimal designs of algorithms. However, the classical time weighted residual approach fails to adequately provide proper extensions to nonlinear dynamics applications. Consequently, the basic premise and argument that is herein advanced is that controllable numerical dissipative time operators designed for linear dynamic problems are very valuable, and are indeed the basis and can be readily employed as the basic parent algorithms, such that when implemented appropriately via the present new time weighted residual representation, they are now readily suitable for extensions to nonlinear dynamics applications. To demonstrate the basic concepts, we consider applications to the Saint Venant Kirchhoff material model simply for illustration, although the method can be readily extended to general material models. The numerical examples presented show that in contrast to the classical time weighted residual approach, which fails to recover the original designs of symplectic-momentum conservation when numerical dissipation is turned off, this new approach readily accomplishes this feature naturally and without enforcing any added constraints, and is the more appropriate way to design a particular class of controllable numerical dissipative schemes. It also leads to algorithm designs that yield fewer numerical oscillations in the energy and angular momentum in contrast to the classical approach, thus additionally confirming the improved effectiveness of the proposed approach. Further, we also show that amongst all the controllable numerical dissipative schemes considered in the sense of and under the framework of LMS methods in the single field form and involving a single solve and second-order time accuracy, the U0- V0optimal is the preferred choice of this particular class of symplectic-momentum conserving based controllable numerical dissipative schemes since: (i) it yields least amount of energy dissipation; and (ii) it is ideal for any given set of initial conditions in the sense that it possesses the highly desirable attributes involving zero order displacement and velocity overshooting behavior. Simple numerical examples are provided that illustrate the fundamental ideas for applications to nonlinear dynamics problems. [ABSTRACT FROM AUTHOR]

We prove a Maillet type theorem for formal solutions of nonlinear difference systems, relating the Gevrey order of the formal solutions to the lowest level of an associated, linear difference operator. [ABSTRACT FROM AUTHOR]

We present a probabilistic analysis of the Floyd–Rivest expected time selection algorithm. In particular, we show that a refinement of the bootstrapped version of the Floyd–Rivest algorithm that determines the C th order statistic by performing an expected n + C + O ( n 1/2 ) comparisons can be made into a randomized algorithm that performs n + C + O ( n 1/2 log 3/2 n ) comparisons with probability at least 1-1/ n ? , for any constant ?>0. [ABSTRACT FROM AUTHOR]

In this article, it is shown that the case for using optimal signal-extraction filters is not all that convincing once it is recognized that seasonal adjustment is typically not the only transformation applied to data. Seasonal adjustment is viewed as any general linear filler. All other data transformations are also assumed to be linear. Although optimal filters always dominate uniform filters, their dominance critically depends on performing seasonal adjustment and the other data transformations in the right sequence. The conclusions of our article make a strong case in favor of the wide practice of uniform filtering. [ABSTRACT FROM AUTHOR]