Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

Numerical Optimization

Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by: (1) solving for correspondences between points on the two shapes; (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; regularized thin-plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearest-neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits, and the COIL data set.

Shape matching and object recognition using shape contexts

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

http://ieeexplore.ieee.org/iel4/557/4025/00695124.pdf

E,//, Signal Design

A Comparison of Two Application-Specific Architectures for 2-d Mesh Computations

Many signal processing algorithms are highly regular, data-independent, and access the data in fixed patterns. For these reasons the current technological advances in very large scale integrated circuits hold especially great promise for signal processing, and in fact we now see the development of many highly integrated processors of a more or less specialized nature. At one end of the spectrum, we see programmable signal processing chips that are really microprocessors, with program, memory and logic separated as in a general purpose machine. At the other extreme, we see highly-specialized, custom chips that perform fixed tasks; typically the data moves through the chip along fixed, regular paths, the arithmetic logic is distributed in space, and the “program” is really “hard-wired” into the topology. This talk is devoted to a study of this latter, custom variety of architecture.

Hierarchical, Parallel and Systolic Array Processing

The authors describe a test method for lattice-gas automata of the type introduced by U. Frisch et al. (1986). The test method consists of inserting test patterns into the initial state of the automaton and using a graphics display to detect errors. The test patterns are carefully constructed limit cycles that are disrupted by errors occurring at any level of the simulator system. The patterns can be run independently to test the system for debugging purposes, or they can be run as sub-simulations embedded in a larger lattice-gas simulation to detect faults at runtime. The authors describe the use of this method on a prototype parallel machine for lattice-gas simulations, and discuss the range of systems that can make use of this type of test method. The test patterns detect all significant one-bit errors. Included are experimental results indicating that multiple bit errors are unlikely to escape detection. >

A practical runtime test method for parallel lattice-gas automata

We present two potentially interesting new venues in all-optical signal processing. First, we demonstrate experimentally that collisions between vector (Manakov-like) solitons involve energy exchange; this feature could be explored for all-optical signal processing. Second, our detailed theoretical studies show how inserting materials that support electro-magnetically induced transparency into microcavities enables design of microcavities with extraordinarily long lifetimes, and enables all-optical signal processing at single photon power levels.

Kenneth Steiglitz

Papers

E,//, Signal Design

A Comparison of Two Application-Specific Architectures for 2-d Mesh Computations

Hierarchical, Parallel and Systolic Array Processing

A practical runtime test method for parallel lattice-gas automata

New windows of opportunity for all-optical information processing: spatial solitons, EIT in microcavities, etc.