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

Despite the fantastic rate at which silicon-based technologies have been progressing, there are several fundamental limitations which suggest that this progress cannot continue without bound. Even within the next decade or two these factors may start to become a real hindrance, and so interest in alternative technologies, such as quantum and DNA computing, has been growing.

Gateless Computing using N-Manakov Solitons

A simple one-pass compiler that translates an intermediate filter language (IFL) into filter code is described. The main motivation is to provide an easy way to experiment with filters for digital sound synthesis. Any realizable, linear, constant-coefficient digital filter can be represented, using two primitive commands. The present version takes less than 250 lines of Pascal and produces Pascal. This compiler is completely portable, requires small computer resources, uses text input that can be generated by other programs, and is easy to modify. As an example of an application, an elaboration of the plucked-string filter is described that produces beat tones in a way similar to FM synthesis. >

A filter compiler for digital sound synthesis

The U.S. Federal Reserve has been steadily shrinking its balance sheet as part of its effort to normalize policy following the financial crisis. Other central banks have announced similar intentions, potentially resulting in the withdrawal of an unprecedented amount of liquidity from the global economy. We propose a modeling framework for analyzing the effects of such policies in which changes in monetary quantities, in particular, the supply and demand for credit, influence economic activity. Persistent dynamics are introduced by explicit modeling of long-term loan obligations held by both the central bank and the financial sector. This introduces a type of path dependence, or "system memory": the current state of the economy, and hence its future trajectory, depends on the sequence of past loans. Shocks or sudden policy shifts can therefore have long-term effects, potentially spanning many years, even in a frictionless setting with complete information available to all agents. An additional feature of the model is that the production of capital is financed, and requires labor as an input. Labor is therefore allocated across two economic sectors: one producing consumer goods, and the other producing capital inputs. We find that (1) The dynamics of a credit expansion and contraction are asymmetric with contractions being more volatile than expansions. Furthermore, expansions and contractions with downward wage friction cause co-movement in unemployment across economic sectors. (2) Shrinking the central bank's balance sheet will not cause a contraction, provided that the financial sector expands credit to compensate for the outgoing monetary flow. (3) Rigidities in the loan portfolio across time cause the real interest rate to vary with inflation -- even in steady state.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID3436518_code2561931.pdf?abstractid=2982988&mirid=1

Credit Shocks, Monetary Flows, and Quantitative Tightening

We describe a test method for lattice-gas automata of the type introduced by Frisch, Hasslacher, and Pomeau. The test method consists of inserting test pattems into the initial state of the automaton and using a graphics display to detect errors. The test pattems are carefully constructed limit cycles that are disrupted by errors occurring at any level of the simulator system. The pattems 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. We 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 pattems detect all significant one-bit errors. We include experimental results indicating that multiple bit errors are unlikely to escape detection.

Kenneth Steiglitz

Papers

Gateless Computing using N-Manakov Solitons

A filter compiler for digital sound synthesis

Credit Shocks, Monetary Flows, and Quantitative Tightening

A practical runtime test method for parallel

A fast error evaluation algorithm for polynomial approximation