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Issue 4 | 1991 | pp. 519-694

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1991

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Select this Article		Inertia-Controlling Methods for General Quadratic Programming P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright SIAM Rev. 33, pp. 1-36 (36 pages) \| Cited 28 times Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract Active-set quadratic programming (QP) methods use a working set to define the search direction and multiplier estimates. In the method proposed by Fletcher in 1971, and in several subsequent mathematically equivalent methods, the working set is chosen to control the inertia of the reduced Hessian, which is never permitted to have more than one nonpositive eigenvalue. (Such methods will be called inertia-controlling.) This paper presents an overview of a generic inertia-controlling QP method, including the equations satisfied by the search direction when the reduced Hessian is positive definite, singular and indefinite. Recurrence relations are derived that define the search direction and Lagrange multiplier vector through equations related to the Karush–Kuhn–Tucker system. Discussion is included of connections with inertia-controlling methods that maintain an explicit factorization of the reduced Hessian matrix.

Select this Article		Searching for New Mathematics Ivars Peterson SIAM Rev. 33, pp. 37-42 (6 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract Nonmathematicians interested in keeping up with contemporary mathematical research face daunting obstacles. The high level of abstraction, unenlightening notation, and the format of journal papers all conspire to make any foray into the mathematical literature frustrating and unrewarding. Mathematicians can do more to make their research accessible to a wider audience.

Select this Article		A Survey of Consistency Properties in Cooperative Game Theory Theo S. H. Driessen SIAM Rev. 33, pp. 43-59 (17 pages) \| Cited 11 times Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract The main purpose of this survey paper is to review the axiomatic characterizations of the Shapley value, the prekernel, the prenucleolus, and the core by means of a consistency property in terms of the reduced games. Whenever possible, new results and new proofs are added.

Select this Article		A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems Manfred Padberg and Giovanni Rinaldi SIAM Rev. 33, pp. 60-100 (41 pages) \| Cited 64 times Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract An algorithm is described for solving large-scale instances of the Symmetric Traveling Salesman Problem (STSP) to optimality. The core of the algorithm is a “polyhedral” cutting-plane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the incidence vectors of the hamiltonian cycles of a complete graph. The cuts are generated by several identification procedures that have been described in a companion paper. Whenever the cutting-plane procedure does not terminate with an optimal solution the algorithm uses a tree-search strategy that, as opposed to branch-and-bound, keeps on producing cuts after branching. The algorithm has been implemented in FORTRAN. Two different linear programming (LP) packages have been used as the LP solver. The implementation of the algorithm and the interface with one of the LP solvers is described in sufficient detail to permit the replication of our experiments. Computational results are reported with up to 42 STSPs with sizes ranging from 48 to 2,392 nodes. Most of the medium-sized test problems are taken from the literature; all others are large-scale real-world problems. All of the instances considered in this study were solved to optimality by the algorithm in “reasonable” computation times.

Select this Article		Establishing Hyperbolic Green’s Functions via Leibniz’s Rule Kurt Kreith SIAM Rev. 33, pp. 101-105 (5 pages) \| Cited 2 times Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract Techniques from the theory of ordinary differential equations are used to characterize fundamental singularities for the wave equation. These lead not only to familiar examples such as the Riemann function, but also to symmetric singularities corresponding to self-adjoint boundary value problems.

Select this Article		Some Comments on the Optimization Problem for Shear Stress Magnitude Stephen P. Huestis SIAM Rev. 33, pp. 106-108 (3 pages) \| Cited 1 time Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract Directions of maximum and minimum shear stress magnitude at a point can be found as solutions to a Lagrange multiplier problem. All three principal shear directions are solutions to the optimization, but only the largest principal shear occurs at a local maximum. The other two principal shears correspond to saddle points for shear stress magnitude. These spurious solutions do not arise if the problem is recast as a Kuhn–Tucker optimization for inequality, rather than equality, constraints.

Select this Article		Source Identification in Remote Sensing Problems John MacBain and Bruce Secrest SIAM Rev. 33, pp. 109-113 (5 pages) \| Cited 1 time Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract In remote sensing problems where a wavefield encounters a scattering body, the source wavelet can be extracted by calculating surface integrals which involve the incident or scattered wavefield. No knowledge of the scattering body is required. The general formulas require the field and its normal derivative; however, some geometries require only the field. The application of the technique to the acoustic marine seismic problem is explored. This paper demonstrates a problem of interest in hydrocarbon exploration where one observes the “solution” of a PDE and must reconstruct the source.

Select this Article		Two Trigonometric Multiple Integrals C. C. Grosjean SIAM Rev. 33, pp. 114-114 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Optimum Multiple Access Coding D. B. Jevtić SIAM Rev. 33, pp. 114-115 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		A Third-Order Differential Equation M. A. Abdelkader SIAM Rev. 33, pp. 115-115 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Limit of a Definite Integral C. A. Oster SIAM Rev. 33, pp. 115-116 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		An Identity for Sums of Binomial Coefficients Masaaki Sibuya SIAM Rev. 33, pp. 116-116 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		An Inequality Wojciech Szatzschneider SIAM Rev. 33, pp. 116-118 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Three Particles Moving on a Circle (Murray S. Klamkin) W. Weston Meyer SIAM Rev. 33, pp. 118-119 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Two Definite Integrals (I. Herron) C. C. Grosjean SIAM Rev. 33, pp. 120-122 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Guerrilla Combat Model (M. A. Abdelkader) Gilbert N. Lewis SIAM Rev. 33, pp. 122-124 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		A Trigonometric Sum (W. Böhm) James A. Wilson SIAM Rev. 33, pp. 124-124 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		An Inequality in Linear Algebra (Petter E. Bjørstad) Boris Mityagin SIAM Rev. 33, pp. 125-127 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Two Trigonometric Multiple Integrals (Quickie) SIAM Rev. 33, pp. 127-128 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		The Riemann Problem and Interaction of Waves in Gas Dynamics (Tung Chang and Ling Hsiao) W. F. Ames SIAM Rev. 33, pp. 129-129 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice, and Algorithms (Max D. Gunzburger) A. J. Baker SIAM Rev. 33, pp. 129-131 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Mathematical Analysis of Nonlinear Dynamic Processes: An Introduction to Processes Governed by Partial Differential Equations (K.-U. Grusa) M. S. Berger SIAM Rev. 33, pp. 131-131 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		An Introduction to Digital Signal Processing (John H. Karl) L. L. Campbell SIAM Rev. 33, pp. 131-132 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Combinatorial Search (Martin Aigner) E. Rodney Canfield SIAM Rev. 33, pp. 132-133 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Numerical Solution of Optimal Control Problems with State Constraints by Sequential Quadratic Programming in Function Spaces (K. C. P. Machielsen) Guanrong Chen SIAM Rev. 33, pp. 133-135 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Partial Differential Equations: Analytical Solution Techniques (J. Kevorkian) Susan Cole SIAM Rev. 33, pp. 135-136 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Mathematical Modelling: A Case Study Approach (R. R. Clements) Ellis Cumberbatch SIAM Rev. 33, pp. 136-136 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Elementary Stability and Bifurcation Theory (Gerard Iooss and Daniel D. Joseph) E. N. Dancer SIAM Rev. 33, pp. 136-137 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Applied Mathematics: A Contemporary Approach (J. David Logan) Paul Davis SIAM Rev. 33, pp. 137-139 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Mathematical Methods and Models in the Biological Sciences Vol. 1 (Martin Eisen) Leah Edelstein-Keshet SIAM Rev. 33, pp. 139-141 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Slope Analysis Using Boundary Elements (Y. S. Jiang) Derek Elsworth SIAM Rev. 33, pp. 141-142 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Stochastic Optimal Control Theory with Application in Self-Tuning Control (K. J. Hunt) G. C. Goodwin SIAM Rev. 33, pp. 142-144 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Numerical Methods and Software (David Kahaner, Cleve Moler, and Stephen Nash) Murli M. Gupta SIAM Rev. 33, pp. 144-147 (4 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Retarded Dynamical Systems: Stability and Characteristic Functions (G. Stépán) Kenneth B. Hannsgen SIAM Rev. 33, pp. 147-147 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Numerical Simulation and Optimal Control in Plasma Physics: With Applications to Tokamaks (Jacques Blum) John L. Johnson SIAM Rev. 33, pp. 147-150 (4 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Mathematical Modeling in Ecology: A Workbook for Students (Clark Jeffries) N. C. Kenkel SIAM Rev. 33, pp. 150-151 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Singular Control Systems (L. Dai) F. L. Lewis SIAM Rev. 33, pp. 151-152 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Stability Analysis of Nonlinear Systems (V. Lakshmikantham, S. Leela, and A. A. Martynyuk) Jean Mawhin SIAM Rev. 33, pp. 152-154 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Multi-Armed Bandit Allocation Indices (J. C. Gittins) Brian P. McCall SIAM Rev. 33, pp. 154-155 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Depth Perception in Frogs and Toads: A Study in Neural Computing (Donald House) John G. Milton SIAM Rev. 33, pp. 155-156 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Roger Temam) Richard E. Mortensen SIAM Rev. 33, pp. 156-158 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Structural Design via Optimality Criteria: The Prager Approach to Structural Optimization (George I. N. Rozvany) Zenon Mroz SIAM Rev. 33, pp. 158-159 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Nonequilibrium Condensation in High-Speed Gas Flows (Yuri A. Ryzhov, Ul’yan G. Pirumov, and Vladimir N. Gorbunov; V. A. Khokhrayakov, trans.) J. R. Ockendon SIAM Rev. 33, pp. 159-160 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		An Introduction to Hilbert Space and Quantum Logic (David W. Cohen) Andrew Vogt SIAM Rev. 33, pp. 160-161 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Continua with Microstructure (Gianfranco Capriz) William O. Williams SIAM Rev. 33, pp. 161-163 (3 pages) \| Cited 2 times Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		New Members SIAM Rev. 33, pp. 164-172 (9 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Elected and Appointed Officials SIAM Rev. 33, pp. 173-173 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

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