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

An analysis of the interchannel crosstalk in time division multiplex systems is given. The results apply to systems with a general linear transmission channel and with arbitrary sampling waveforms. The general result is obtained in closed form. This is then applied to the particular case of multiplexing with rectangular waveforms and a single pole transmission channel. A normalized plot of crosstalk vs system parameters for such systems is presented.

Crosstalk in Time Division Multiplex Systems

Using Circulant Markov Chains to Generate Waveforms for Music

In this paper we study the transfer of information between colliding solitary waves. By this we mean the following: The state of a solitary wave is a set of parameters, such as amplitude, width, velocity, or phase, that can change during collisions. We say information is transferred during a collision of solitary waves A and B if the state of B after the collision depends on the state of A before the collision. This is not the case in the cubic

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Information transfer between solitary waves in the saturable Schrödinger equation

We study the problem of optimizing the pulldown diffusion widths in the one-bit full adder when it is embedded in a regular array, using the simplest possible array multiplier with a delay-time criterion as an example. A local optimization algorithm is used, which varies two parameters at a time along the critical path until a local optimum is found. The analysis routines include the Berkeley tools [10] and the Princeton procedural layout language ALLENDE [11- 12]. Two ways are suggested for optimizing large arrays in practical amounts of time. First, the full-adder cell optimized within a minimum-size array can be used in the large array. This is a good choice because the interior cells of the small prototype have the same boundary conditions as those in the larger array. A second, even faster, method is to approximate the delay time from some simple assumptions about the critical path. Numerical results show that both these methods are effective. We give typical local optima obtained when delay time is minimized, together with power-time tradeoff curves, for the 3×3 and 4×4 array multipliers, using 4µ (λ=2µ) nMOS fabrication parameters, and a 5- parameter random-logic full-adder cell.

Time-power-area tradeoffs for the nMOS VLSI full-adder

We derive the interlacing properties of the eigenvalues of a symmetric matrix with those of its largest principal submatrix using root-locus ideas. We then give a sufficient condition for distinctness of eigenvalues based on the minimality of an associated linear system.

Kenneth Steiglitz

Papers

Crosstalk in Time Division Multiplex Systems

Using Circulant Markov Chains to Generate Waveforms for Music

Information transfer between solitary waves in the saturable Schrödinger equation

Time-power-area tradeoffs for the nMOS VLSI full-adder

Eigenvalues of symmetric matrices: System theory conditions for distinctness