Stanford University Department of Operations Research Systems Optimization LaboratoryOverview
Publication Timeline
Most widely held works by
Stanford University
Modeling water supply for the energy sector : final report
by Nathan Buras
(
Book
)
1 edition published in 1982 in English and held by 11 WorldCat member libraries worldwide
PILOT1980 energyeconomic model
by George B Dantzig
(
Book
)
1 edition published in 1982 in English and held by 10 WorldCat member libraries worldwide
Determining the feasibility of incorporating water resource constraints into energy models : final report
by Nathan Buras
(
Book
)
2 editions published in 1979 in English and held by 10 WorldCat member libraries worldwide
Stanford PILOT energy/economic model : interim report
by George B Dantzig
(
Book
)
2 editions published between 1977 and 1978 in English and held by 6 WorldCat member libraries worldwide The PILOT Energy Modeling Project is concerned with: (1) performing modeling and methodology research dealing with construction and solution of reasonably large scale mathematical programming models of energy/economic systems; (2) using modeling research towards analysis of some of today's important energy questions; and (3) using the modeling and methodology to construct better models for improved analysis of tomorrow's important energy questions. At the core of this project is the development of a multisector, intertemporal linear programming modeling system that describes in physical terms many of the technological interactions within and across the sectors of the American economy. The general aim of the modeling effort is to permit studies to assess (1) how specific energy policies will affect the energy supply/demand picture and (2) how the physical capacity of the economy over the next 3035 years to provide goods and services to its populace could be affected by changes in energy supply. Intertemporal linear programming models of the energy sector and the economy provide a unique medium for exploring future energy policy options
MINOS : a largescale nonlinear programming system (for problems with linear constraints) user's guide
by Bruce A Murtagh
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Book
)
3 editions published in 1977 in English and held by 4 WorldCat member libraries worldwide MINOS is a Fortran program designed to minimize a linear or nonlinear function subject to linear constraints, where the constraint matrix is in general assumed to be large and sparse. The User's Guide contains an overview of the MINOS System, including descriptions of the theoretical algorithms as well as the details of implementation. The Guide also provides complete instructions for the use of MINOS, and illustrates the diversity of application by several examples. (Author)
Mathematical decomposition techniques for power system expansion planning : final report
(
Book
)
1 edition published in 1988 in English and held by 4 WorldCat member libraries worldwide
Planning under uncertainty using parallel computing
by George B Dantzig
(
Book
)
1 edition published in 1987 in English and held by 4 WorldCat member libraries worldwide For example, parallel processors may make it possible to come to better grips with the fundamental problems of planning, scheduling, design, and control of complex systems such as the economy, an industrial enterprise, an energy system, a waterresource system, military models for planningandcontrol, decisions about investment, innovation, employment, and healthdelivery systems."
Stanford Pilot energy/economic model : interim report, May, 1978
by George B Dantzig
(
Book
)
2 editions published in 1978 in English and held by 4 WorldCat member libraries worldwide
Optimal design of pitched tapered laminated wood beams
by M Avriel
(
Book
)
2 editions published in 1976 in English and held by 4 WorldCat member libraries worldwide The optimal design of a pitched tapered laminated woood beam is considered. An engineering formulation is given in which the volume of the beam is minimized. The problem is then reformulated and solved as a generalized geometric (signomial) program. Sample designs are presented. (Author)
Planning under uncertainty : solving largescale stochastic linear programs
by Gerd Infanger
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)
3 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide For many practical problems, solutions obtained from deterministic models are unsatisfactory because they fail to hedge against certain contingencies that may occur in the future. Stochastic models address this shortcoming, but up to recently seemed to be intractable due to their size. Recent advances both in solution algorithms and in computer technology now allow us to solve important and general classes of practical stochastic problems. We show how largescale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo (importance) sampling techniques. We discuss the methodology for solving twostage stochastic linear programs with recourse, present numerical results of large problems with numerous stochastic parameters, show how to efficiently implement the methodology on a parallel multicomputer and derive the theory for solving a general class of multistage problems with dependency of the stochastic parameters within a stage and between different stages
An analysis of an available set of linear programming test problems
by Irvin J Lustig
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Book
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1 edition published in 1987 in English and held by 3 WorldCat member libraries worldwide Abstract: "A set of linear programming test problems is analyzed with MINOS, Version 5.1. The problems have been run with different options for scaling and partial pricing to illustrate the effects of these options on the performance of the simplex method. The results indicate that the different options can significantly improve or degrade the performance of the simplex method, and that these options must be chosen wisely. For each problem, a picture of the nonzero structure of the matrix A is also presented so that the problems can be classified according to structure."
Largescale sequential quadratic programming algorithms
by Stanford University
(
)
3 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to largescale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasiNewton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reducedgradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal nullspace basis for largescale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an activeset method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems
Managing an oil bonanza an analysis of alternative Mexican export policies
by Stanford University
(
Book
)
2 editions published in 1980 in English and held by 3 WorldCat member libraries worldwide
Parallel processors for planning under uncertainty
by George B Dantzig
(
Book
)
2 editions published between 1988 and 1989 in English and held by 3 WorldCat member libraries worldwide Abstract: "In this paper we describe joint research under way by Mordecai Avriel, Robert Entriken, and the authors. Our goal is to demonstrate, for an important class of multistage stochastic models, that a variety of techniques for solving largescale linear programs can be effectively mixed to attack this fundamental problem. The ideas involve nested primal and dual decomposition, combined with Monte Carlo simulation, high speed importance sampling, and quadrature methods for numerical integration, together with the use [of] parallel processors."
Using MINOS as a subroutine for decomposition
by Stanford University
(
Book
)
2 editions published in 1987 in English and held by 3 WorldCat member libraries worldwide Abstract: "The marriage of technology and computers has given birth to the present information age of man. Previously unheardof computational power is now within the grasp of even a child, at an arcade. Our most astonishing accomplishments are complex products of technology, often heralded by advances in computers. So will the advent of parallel processors mark the beginning of even greater technological advances. Today's unheardof will soon become tomorrow's child's play. This is a report on the first step towards the goal of solving linear programs by decomposition on a parallel computer. It outlines the use of MINOS as a solver for optimization subproblems that will eventually appear on the separate processors of a parallel computer
Computing modified newton directions using a partial Cholesky factorization
by Stanford University
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)
3 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide The effectiveness of Newton's method for finding an unconstrained minimizer of a strictly convex twice continuously differentiable function has prompted the proposal of various modified Newton inetliods for the nonconvex case. Linesearch modified Newton methods utilize a linear combination of a descent direction and a direction of negative curvature. If these directions are sufficient in a certain sense, and a suitable linesearch is used, the resulting method will generate limit points that satisfy the secondorder necessary conditions for optimality. We propose an efficient method for computing a descent direction and a direction of negative curvature that is based on a partial Cholesky factorization of the Hessian. This factorization not only gives theoretically satisfactory directions, but also requires only a partial pivoting strategy, i.e., the equivalent of only two rows of the Schur complement need be examined at each step
Origins of the simplex method
by George B Dantzig
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Book
)
1 edition published in 1987 in English and held by 3 WorldCat member libraries worldwide Abstract: "In the summer of 1947, when I first began to work on the simplex method for solving linear programs, the first idea that occurred to me is one that would occur to any trained mathematician, namely the idea of step by step descent (with respect to the objective function) along edges of the convex polyhedral set from one vertex to an adjacent one. I rejected this algorithm outright on intuitive grounds  it had to be inefficient because it proposed to solve the problem by wandering along some path of outside edges until the optimal vertex was reached. I therefore began to look for other methods which gave more promise of being efficient, such as those that went directly through the interior, [1]
Determining the feasibility of integrating water resource constraints into energy models
by Stanford University
(
Book
)
2 editions published in 1979 in English and held by 3 WorldCat member libraries worldwide
Comparisons of composite simplex algorithms
by Stanford University
(
Book
)
2 editions published in 1987 in English and held by 3 WorldCat member libraries worldwide The implementations of each algorithm are also discussed. One theme that is present throughout all of the computational experience is that there is no one algorithm which is the best algorithm for all problems."
Computational behavior of GaussNewton methods
by Christina Fraley
(
Book
)
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide Abstract: "This paper is concerned with the behavior of GaussNewton methods for nonlinear leastsquares problems. Here we assume that the defining feature of a GaussNewton method is that the direction from one iterate to the next is the numerical solution of a particular linear leastsquares problem, with a steplength subsequently determined by a linesearch procedure. It is well known that GaussNewton methods cannot be successfully applied to nonlinear leastsquares problems as a class without modification. Our purpose is to give specific examples illustrating some of the difficulties that arise in practice which we believe have not been fully described in the literature." more
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Associated Subjects
Decomposition (Mathematics) Energy policyEconomic aspects ExportsGovernment policy Gaussian processes Industrial water supplyMathematical models Laminated wood Least squares Linear programming Mathematical optimizationComputer programs Mexico Nonlinear programming Nonlinear programmingData processing Parallel processing (Electronic computers) PetroleumGovernment policy Power resourcesMathematical models Production scheduling Programming (Mathematics) Simplexes (Mathematics) Stochastic processes Stochastic programming United States Water resources developmentMathematical models WatersupplyMathematical models

Alternative Names
S.O.L.
SOL
SOL Abkuerzung
Stanford University Department of Operations Research Systems Optimization Laboratory
Stanford University. Dept. of Operations Research. Systems Optimization Laboratory
Stanford University Stanford, Calif Systems Optimization Laboratory
Stanford University Systems Optimization Laboratory
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