Search

For quasi-Newton methods in unconstrained minimization, it is valuable to develop methods that are robust, i.e., methods that converge on a large number of problems. Trust-region algorithms are often regarded to be more robust than line-search methods, however, because trust-region methods are computationally more expensive, the most popular quasi-Newton implementations use line-search methods. To fill this gap, we develop a trust-region method that updates an $LDL^T$ factorization, scales quadratically with the size of the problem, and is competitive with a conventional line-search method.

Projected-search methods for bound-constrained optimization are based on performing a search along a piecewise-linear continuous path obtained by projecting a search direction onto the feasible region. A benefit of these methods is that many changes to the active set can be made at the cost of computing a single search direction. As the objective function is not differentiable along the search path, it is not possible to use a projected-search method with a step that satisfies the Wolfe conditions, which require the directional derivative of the objective function at a point on the path. Thus, methods based on a simple backtracking procedure must be used to give a step that satisfies an "Armijo-like" sufficient decrease condition. As a consequence, conventional projected-search methods are unable to exploit sophisticated safeguarded polynomial interpolation techniques that have been shown to be effective for the unconstrained case. This paper concerns the formulation and analysis of projected-search methods based on a new quasi-Wolfe line search that is appropriate for piecewise differentiable functions. The behavior of the line search is similar to conventional Wolfe line search, except that a step is accepted under a wider range of conditions. These conditions take into consideration steps at which the restriction of the objective function on the search path is not differentiable. Two new classes of method are proposed that may be broadly categorized as active-set and interior-point methods. Computational results are given for two specific methods from these general classes: a projected-search active-set method that uses a limited-memory quasi-Newton approximation of the Hessian; and a projected-search primal-dual interior-point method. The results show that in these contexts, a quasi-Wolfe line search is substantially more efficient and reliable than an Armijo line search.

Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables. In the first part of the paper, two methods are proposed, one primal and one dual. These methods generate a sequence of iterates that are feasible with respect to the equality constraints associated with the optimality conditions of the primal-dual form. The primal method maintains feasibility of the primal inequalities while driving the infeasibilities of the dual inequalities to zero. The dual method maintains feasibility of the dual inequalities while moving to satisfy the primal inequalities. In each of these methods, the search directions satisfy a KKT system of equations formed from Hessian and constraint components associated with an appropriate column basis. The composition of the basis is specified by an active-set strategy that guarantees the nonsingularity of each set of KKT equations. Each of the proposed methods is a conventional active-set method in the sense that an initial primal- or dual-feasible point is required. In the second part of the paper, it is shown how the quadratic program may be solved as a coupled pair of primal and dual quadratic programs created from the original by simultaneously shifting the simple-bound constraints and adding a penalty term to the objective function. Any conventional column basis may be made optimal for such a primal-dual pair of shifted-penalized problems. The shifts are then updated using the solution of either the primal or the dual shifted problem. An obvious application of this approach is to solve a shifted dual QP to define an initial feasible point for the primal (or vice versa). The computational performance of each of the proposed methods is evaluated on a set of convex problems., Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s10107-015-0966-2

This paper highlights some of the issues that arose during the drafting of a revised version of the IFLA (International Federation of Library Associations and Institutions) Guidelines for Public Libraries. The sections of the new document are outlined as follows: (1) The Role and Purpose of the Public Library; (2) The Legal and Financial Framework; (3) Meeting the Needs of the Users; (4) Collection Development; (5) Human Resources; and (6) The Management and Marketing of the Public Library. Three key roles of the public library (i.e., education, information, and personal development) are discussed. Other issues addressed include: the importance of determining priorities; competition with other organizations; changes due to developments in information technology; access to information and communications technology; community needs analysis; customer care; development of collection standards; effective leadership; and marketing and promotion. (MES)

SnadiOpt is a package that supports the use of the automatic differentiation package ADIFOR with the optimization package Snopt. Snopt is a general-purpose system for solving optimization problems with many variables and constraints. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for large-scale linear and quadratic programming and for linearly constrained optimization, as well as for general nonlinear programs. The method used by Snopt requires the first derivatives of the objective and constraint functions to be available. The SnadiOpt package allows users to avoid the time-consuming and error-prone process of evaluating and coding these derivatives. Given Fortran code for evaluating only the values of the objective and constraints, SnadiOpt automatically generates the code for evaluating the derivatives and builds the relevant Snopt input files and sparse data structures., Comment: pages i-iv, 1-23