Abstract. We propose a simple approach to combining first-order logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a first-order knowledge base with a weight attached to each formula (or clause). Together with a set of constants representing objects in the domain, it specifies a ground Markov network containing one feature for each possible grounding of a first-order formula in the KB, with the corresponding weight. Inference in MLNs is performed by MCMC over the minimal subset of the ground network required for answering the query. Weights are efficiently learned from relational databases by iteratively optimizing a pseudo-likelihood measure. Optionally, additional clauses are learned using inductive logic programming techniques. Experiments with a real-world database and knowledge base in a university domain illustrate the promise of this approach.

Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse.

The purpose of this paper is to discuss the scope and functionality of a versatile environment for testing small and large-scale nonlinear optimization algorithms. Although many of these facilities were originally produced by the authors in conjunction with the software package LANCELOT, we believe that they will be useful in their own right and should be available to researchers for their development of optimization software. The tools are available by anonymous ftp from a number of sources and may, in many cases, be installed automatically. The scope of a major collection of test problems written in the standard input format (SIF) used by the LANCELOT software package is described. Recognising that most software was not written with the SIF in mind, we provide tools to assist in building an interface between this input format and other optimization packages. These tools already provide a link between the SIF and an number of existing packages, including MINOS and OSL. In ad...

We derive compact representations of BFGS and symmetric rank-one matrices for optimization. These representations allow us to efficiently implement limited memory methods for large constrained optimization problems. In particular, we discuss how to compute projections of limited memory matrices onto subspaces. We also present a compact representation of the matrices generated by Broyden's update for solving systems of nonlinear equations. Key words: Quasi-Newton method, constrained optimization, limited memory method, large-scale optimization. Abbreviated title: Representation of quasi-Newton matrices. 1. Introduction. Limited memory quasi-Newton methods are known to be effective techniques for solving certain classes of large-scale unconstrained optimization problems (Buckley and Le Nir (1983), Liu and Nocedal (1989), Gilbert and Lemar'echal (1989)) . They make simple approximations of Hessian matrices, which are often good enough to provide a fast rate of linear convergence, and re...

Optimization problems involving eigenvalues arise in many applications. Let x be a vector of real parameters and let A(x) be a continuously differentiable symmetric matrix function of x. We consider a particular problem which occurs frequently: the minimization of the maximum eigenvalue of A(x), subject to linear constraints and bounds on x. The eigenvalues of A(x) are not differentiable at points x where they coalesce, so the optimization problem is said to be nonsmooth. Furthermore, it is typically the case that the optimization objective tends to make eigenvalues coalesce at a solution point. There are three main purposes of the paper. The first is to present a clear and self-contained derivation of the Clarke generalized gradient of the max eigenvalue function in terms of a "dual matrix". The second purpose is to describe a new algorithm, based on the ideas of a previous paper by the author (SIAM J. Matrix Anal. Appl. 9 (1988) 256-268), which is suitable for solving l...

The problem of finding a point that satisfies the sufficient decrease and curvature condition is formulated in terms of finding a point in a set T (). We describe a search algorithms for this problem that produces a sequence of iterates that converge to a point in T () and that, except for pathological cases, terminates in a finite number of steps. Numerical results for an implementation of the search algorithm on a set of test functions show that the algorithm terminates within a small number of iterations. LINE SEARCH ALGORITHMS WITH GUARANTEED SUFFICIENT DECREASE Jorge J. Mor'e and David J. Thuente 1 Introduction Given a continuously differentiable function OE : IR ! IR defined on [0; 1) with OE 0 (0) ! 0, and constants and j in (0; 1), we are interested in finding an ff ? 0 such that OE(ff) OE(0) + OE 0 (0)ff (1:1) and jOE 0 (ff)j jjOE 0 (0)j: (1:2) The development of a search procedure that satisfies these conditions is a crucial ingredient in a line search meth...

Search engine advertising has become a significant element of the Web browsing experience. Choosing the right ads for the query and the order in which they are displayed greatly affects the probability that a user will see and click on each ad. This ranking has a strong impact on the revenue the search engine receives from the ads. Further, showing the user an ad that they prefer to click on improves user satisfaction. For these reasons, it is important to be able to accurately estimate the click-through rate of ads in the system. For ads that have been displayed repeatedly, this is empirically measurable, but for new ads, other means must be used. We show that we can use features of ads, terms, and advertisers to learn a model that accurately predicts the click-though rate for new ads. We also show that using our model improves the convergence and performance of an advertising system. As a result, our model increases both revenue and user satisfaction.

this article I will attempt to review the most recent advances in the theory of unconstrained optimization, and will also describe some important open questions. Before doing so, I should point out that the value of the theory of optimization is not limited to its capacity for explaining the behavior of the most widely used techniques. The question

We investigate prototype-driven learning for primarily unsupervised sequence modeling. Prior knowledge is specified declaratively, by providing a few canonical examples of each target annotation label. This sparse prototype information is then propagated across a corpus using distributional similarity features in a log-linear generative model. On part-of-speech induction in English and Chinese, as well as an information extraction task, prototype features provide substantial error rate reductions over competitive baselines and outperform previous work. For example, we can achieve an English part-of-speech tagging accuracy of 80.5 % using only three examples of each tag and no dictionary constraints. We also compare to semi-supervised learning and discuss the system’s error trends. 1

Abstract. This paper describes a software implementation of Byrd and Omojokun’s trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques for solving the subproblems occurring in the algorithm. Second derivative information can be used, but when it is not available, limited memory quasi-Newton approximations are made. The performance of the code is studied using a set of difficult test problems from the CUTE collection.