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

We show that the FHP lattice gases are computation universal, implying that general questions about their behavior are undecidable. The proof embeds a universal one-dimensional cellular automat on in the two-dimensional FHP latt ice gas. This provides evidence that general questions about fluid behavior are undecidable.

Two-Dimensional FHP Lattice Gases Are Computation Universal.

A central problem in the production of music by computer is how to generate sounds with similar but different timbres; that is, how to synthesize a "family" of instruments that are perceived as distinguishable but similar in timbre. This paper describes a method for synthesizing a family of string-like instruments that proceeds as follows: First, a few actual violin notes are analyzed using linear prediction. Second, a bilinear transformation is applied to the linear prediction model on synthesis, using a recently described algorithm. This yields a computationally efficient way to generate a virtual string orchestra, with violin-, viola-, violoncello-, and bass-like timbres. A realization of a 4.7-minute piece composed by P. Lansky will be played.

Synthesis of timbral families by warped linear prediction

Functional Algorithm Simulation is a methodology for predicting the computation and communication characteristics of parallel algorithms for a class of scientific problems, without actually performing the expensive numerical computations involved. In this paper, we use Functional Algorithm Simulation to study the parallel Fast Multipole Method (FMM), which solves the N-body problem. Functional Algorithm Simulation provides us with useful information regarding communication patterns in the algorithm, the variation of available parallelism during different algorithmic phases, and upper bounds on available speedups for different problem sizes. Furthermore, it allows us to predict the performance of the FMM on message-passing multiprocessors with topologies such as cliques, hypercubes, rings, and multirings, over a wider range of problem sizes and numbers of processors than would be feasible by direct simulation. Our simulations show that an implementation of the FMM on low-cost, scalable ring or multiring architectures can attain satisfactory performance.

Functional algorithm simulation of the fast multipole method : Architectural implications

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Computing with Solitons

Abstruct- We consider transmission of data over multiple coupled channels, such as bundles of twisted-pair copper wires in the local sub- scriber loop, and between central offices in the public switched tele- phone network. Transceiver designs for such channels typically treat the crosstalk between adjacent twisted pairs as random noise uncorrelated with the transmitted signal. We propose a transmitterheceiver pair that compensates for crosstalk by treating an entire bundle of twisted pairs as a single multiinput~ultioutput channel with a (slowly varying) matrix transfer function. The proposed transceiver uses multichannel adap- tive FIR filters to cancel near- and far-end crosstalk, and to pre- and postprocess the input/output of the channel. The linear pre- and post- processors that minimize mean squared error between the received and transmitted signal in the presence of both near- and far-end crosstalk are derived. The performance of an adaptive near-end crosstalk canceller using the stochastic gradient (LMS) transversal algorithm is illustrated via numerical simulation. Plots of mean squared error versus time and eye diagrams are presented assuming a standard transmission line model for the channel. A signal design algorithm that maps a vector input bit stream to a stream of channel symbol vectors is also presented. This algorithm is illustrated explicitly for a simple model of two coupled channels. It is shown that the achievable rate using the proposed signaling scheme is very close to the rate attainable in the absence of far-end crosstalk, and is significantly greater than the achievable rate assuming that far-end crosstalk is treated as additive noise with unknown statistics.

Kenneth Steiglitz

Papers

Two-Dimensional FHP Lattice Gases Are Computation Universal.

Synthesis of timbral families by warped linear prediction

Functional algorithm simulation of the fast multipole method : Architectural implications

Computing with Solitons

Multichannel Signal Processing