Nonlinear Stepsize Control, Trust Regions and Regularizations for Unconstrained Optimization

A general class of algorithms for unconstrained optimization is introduced, which subsumes the classical trust-region algorithm and two of its newer variants, as well as the cubic and quadratic regularization methods. A unified theory of global convergence to first-order critical points is then described for this class. An extension to projection-based trust-region algorithms for nonlinear … Read more

A Cutting Surface Method for Uncertain Linear Programs with Polyhedral Stochastic Dominance Constraints

In this paper we study linear optimization problems with multi-dimensional linear positive second-order stochastic dominance constraints. By using the polyhedral properties of the second- order linear dominance condition we present a cutting-surface algorithm, and show its finite convergence. The cut generation problem is a difference of convex functions (DC) optimization problem. We exploit the polyhedral … Read more

Proximal Methods for Nonlinear Programming: Double Regularization and Inexact Subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that … Read more

Cutting Plane Algorithms for 0-1 Programming Based on Cardinality Cuts

Abstract: We present new valid inequalities for 0-1 programming problems that work in similar ways to well known cover inequalities. Discussion and analysis of these cuts is followed by their revision and use in integer programming as a new generation of cuts that excludes not only portions of polyhedra containing noninteger points, also parts with … Read more

A genetic algorithm for a global optimization problem arising in the detection of gravitational waves

The detection of gravitational waves is a long-awaited event in modern physics and, to achieve this challenging goal, detectors with high sensitivity are being used or are under development. In order to extract gravitational signals, emitted by coalescing binary systems of compact objects (neutron stars and/or black holes), from noisy data obtained by interferometric detectors, … Read more

Support vector machines with the ramp loss and the hard margin loss

In the interest of deriving classifiers that are robust to outlier observations, we present integer programming formulations of Vapnik’s support vector machine (SVM) with the ramp loss and hard margin loss. The ramp loss allows a maximum error of 2 for each training observation, while the hard margin loss calculates error by counting the number … Read more