Jonathan Eckstein The NP-hard Maximum Monomial Agreement (MMA) problem consists of finding a single logical conjunction that best fits a weighted dataset of “positive” and “negative” binary vectors. Computing classifiers using boosting methods involves a maximum agreement subproblem at each iteration, although such subproblems are typically solved by heuristic methods. Here, we describe an exact branch and … Read more
In optimization-based classification model selection, for example when using linear programming formulations, a standard approach is to penalize the L1 norm of some linear functional in order to select sparse models. Instead, we propose a novel integer linear program for sparse classifier selection, generalizing the minimum disagreement hyperplane problem whose complexity has been investigated in … Read more
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
We describe scheduling algorithms for monitoring an information source whose contents change at times modeled by a nonhomogeneous Poisson process. In a given time period of length T, we enforce a politeness constraint that we may only probe the source at most n times. This constraint, along with an optional constraint that no two probes … Read more
We consider the variational inequality problem formed by a general set-valued maximal monotone operator and a possibly unbounded “box” in $R^n$, and study its solution by proximal methods whose distance regularizations are coercive over the box. We prove convergence for a class of double regularizations generalizing a previously-proposed class of Auslender et al. We apply … Read more
Given two finite sets of points $X^+$ and $X^-$ in $\R^n$, the maximum box problem consists in finding an interval (“box”) $B=\{x : l \leq x \leq u\}$ such that $B\cap X^-=\emptyset$, and the cardinality of $B\cap X^+$ is maximized. A simple generalization can be obtained by instead maximizing a weighted sum of the elements … Read more
We present a heuristic method for general 0-1 mixed integer programming, intended for eventual incorporation into parallel branch-and-bound methods for solving such problems exactly. The core of the heuristic is a rounding method based on simplex pivots, employing only gradient information, for a strictly concave, differentiable merit function measuring integer feasibility. When local minima of … Read more
This paper demonstrates that for generalized methods of multipliers for convex programming based on Bregman distance kernels — including the classical quadratic method of multipliers — the minimization of the augmented Lagrangian can be truncated using a simple, generally implementable stopping criterion based only on the norms of the primal iterate and the gradient (or … Read more