Stanford University Systems Optimization Laboratory
Overview
Works:  113 works in 125 publications in 1 language and 237 library holdings 

Roles:  Researcher 
Publication Timeline
.
Most widely held works by
Stanford University
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
2 editions published in 1979 in English and held by 10 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
1 edition published in 1982 in English and held by 10 WorldCat member libraries worldwide
Modeling water supply for the energy sector : final report by
N Buras(
Book
)
1 edition published in 1982 in English and held by 10 WorldCat member libraries worldwide
1 edition published in 1982 in English and held by 10 WorldCat member libraries worldwide
Stanford PILOT energy/economic model : interim report by
George B Dantzig(
Book
)
1 edition published in 1978 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1978 in English and held by 5 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."
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."
MINOS : a largescale nonlinear programming system (for problems with linear constraints) user's guide by
Bruce A Murtagh(
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)
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)
Stanford Pilot energy/economic model : interim report, May, 1978 by
George B Dantzig(
Book
)
1 edition published in 1978 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1978 in English and held by 3 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 3 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)
2 editions published in 1976 in English and held by 3 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)
An analysis of an available set of linear programming test problems by Irvin J Lustig(
Book
)
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."
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."
Origins of the simplex method by
George B Dantzig(
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]
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]
Sufficient matrices and the linear complementarity problem by
Richard Cottle(
Book
)
2 editions published in 1987 in English and held by 2 WorldCat member libraries worldwide
Abstract: "In this paper we pose and answer two questions about solutions of the linear complementarity problem (LCP). The first question is concerned with the conditions on a square matrix M which quarantee that for every vector q, the solutions of LCP (q, M) are identical to the KarushKuhnTucker points of the natural quadratic program associated with (q, M). In answering this question we introduce the class of 'row sufficient' matrices. The transpose of such a matrix is what we call 'column sufficient.' The latter matrices turn out to furnish the answer to our second question which asks for the conditions on M under which the solution set of (q, M) is convex for every q. In addition to these two main results, we discuss the connections of these two new matrix classes with other wellknown matrix classes in linear complementarity theory."
2 editions published in 1987 in English and held by 2 WorldCat member libraries worldwide
Abstract: "In this paper we pose and answer two questions about solutions of the linear complementarity problem (LCP). The first question is concerned with the conditions on a square matrix M which quarantee that for every vector q, the solutions of LCP (q, M) are identical to the KarushKuhnTucker points of the natural quadratic program associated with (q, M). In answering this question we introduce the class of 'row sufficient' matrices. The transpose of such a matrix is what we call 'column sufficient.' The latter matrices turn out to furnish the answer to our second question which asks for the conditions on M under which the solution set of (q, M) is convex for every q. In addition to these two main results, we discuss the connections of these two new matrix classes with other wellknown matrix classes in linear complementarity theory."
The Box Method for linear programming by Karel Zikan(
Book
)
2 editions published in 1987 in English and held by 2 WorldCat member libraries worldwide
Abstract: "A crucial aspect of the Box Method for linear programming is the finding of a 'minimumweight basis' corresponding to a given interior feasible point. This subproblem leads to the formation of the 'Box Problem, ' a special linear program having a closed form solution which provides the search direction at the current iteration. Finding a minimumweight basis is a matroidal (or, combinatorial) optimization problem that can be handled by a greedy algorithm. This paper suggests a way of efficiently solving the minimumweight basis problem in cases where the (primal, standard form) linear program contains explicitly bounded variables
2 editions published in 1987 in English and held by 2 WorldCat member libraries worldwide
Abstract: "A crucial aspect of the Box Method for linear programming is the finding of a 'minimumweight basis' corresponding to a given interior feasible point. This subproblem leads to the formation of the 'Box Problem, ' a special linear program having a closed form solution which provides the search direction at the current iteration. Finding a minimumweight basis is a matroidal (or, combinatorial) optimization problem that can be handled by a greedy algorithm. This paper suggests a way of efficiently solving the minimumweight basis problem in cases where the (primal, standard form) linear program contains explicitly bounded variables
The Principal Pivoting Method revisited by
Richard Cottle(
Book
)
2 editions published in 1989 in English and held by 2 WorldCat member libraries worldwide
Abstract: "The Principal Pivoting Method (PPM) for the Linear Complementarity Problem (LCP) is shown to be applicable to the class of LCPs involving the newly identified class of sufficient matrices."
2 editions published in 1989 in English and held by 2 WorldCat member libraries worldwide
Abstract: "The Principal Pivoting Method (PPM) for the Linear Complementarity Problem (LCP) is shown to be applicable to the class of LCPs involving the newly identified class of sufficient matrices."
Simplex algorithm with a new primal and dual pivot rule by
Stanford University(
)
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
We present a simplextype algorithm for linear programming that works with primalfeasible and dualfeasible points associated with bases that differ by only one column
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
We present a simplextype algorithm for linear programming that works with primalfeasible and dualfeasible points associated with bases that differ by only one column
On the numerical stability of quasidefinite systems by
Stanford University(
)
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
The authors discuss the solution of sparse linear equations Kd = r, where K is a symmetric and specially structured indefinite matrix that often arises in numerical optimization. For such K, the indefinite factorization K = LDL{sup T} is known to exist in exact arithmetic with 1 x 1 pivots and no row or column interchanges. It is shown that the stability of the LDL{sup T} factorization of this matrix is naturally connected with the stability of the LDM{sup T} factorization of a closely related unsymmetric positivedefinite matrix. Conditions are given that allow the stable numerical solution of this system by Gaussian elimination without row and column interchanges
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
The authors discuss the solution of sparse linear equations Kd = r, where K is a symmetric and specially structured indefinite matrix that often arises in numerical optimization. For such K, the indefinite factorization K = LDL{sup T} is known to exist in exact arithmetic with 1 x 1 pivots and no row or column interchanges. It is shown that the stability of the LDL{sup T} factorization of this matrix is naturally connected with the stability of the LDM{sup T} factorization of a closely related unsymmetric positivedefinite matrix. Conditions are given that allow the stable numerical solution of this system by Gaussian elimination without row and column interchanges
Two Characterizations of Sufficient Matrices(
)
1 edition published in 1990 in English and held by 0 WorldCat member libraries worldwide
Two characterizations are given for the class of sufficient matrices defined by Cottle, Pang, and Venkateswaran. The first is a direct translation of the definition into linear programming terms. The second can be thought of as a generalization of a theorem of T.D. Parsons on Pmatrices. 19 refs
1 edition published in 1990 in English and held by 0 WorldCat member libraries worldwide
Two characterizations are given for the class of sufficient matrices defined by Cottle, Pang, and Venkateswaran. The first is a direct translation of the definition into linear programming terms. The second can be thought of as a generalization of a theorem of T.D. Parsons on Pmatrices. 19 refs
Decomposition and (importance) sampling techniques for multistage stochastic linear programs by
Stanford University(
)
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
The difficulty of solving largescale multistage stochastic linear programs arises from the sheer number of scenarios associated with numerous stochastic parameters. The number of scenarios grows exponentially with the number of stages and problems get easily out of hand even for very moderate numbers of stochastic parameters per stage. Our method combines dual (Benders) decomposition with Monte Carlo sampling techniques. We employ importance sampling to efficiently obtain accurate estimates of both expected future costs and gradients and righthand sides of cuts. The method enables us to solve practical largescale problems with many stages and numerous stochastic parameters per stage. We discuss the theory of sharing and adjusting cuts between different scenarios in a stage. We derive probabilistic lower and upper bounds, where we use importance path sampling for the upper bound estimation. Initial numerical results turned out to be promising
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
The difficulty of solving largescale multistage stochastic linear programs arises from the sheer number of scenarios associated with numerous stochastic parameters. The number of scenarios grows exponentially with the number of stages and problems get easily out of hand even for very moderate numbers of stochastic parameters per stage. Our method combines dual (Benders) decomposition with Monte Carlo sampling techniques. We employ importance sampling to efficiently obtain accurate estimates of both expected future costs and gradients and righthand sides of cuts. The method enables us to solve practical largescale problems with many stages and numerous stochastic parameters per stage. We discuss the theory of sharing and adjusting cuts between different scenarios in a stage. We derive probabilistic lower and upper bounds, where we use importance path sampling for the upper bound estimation. Initial numerical results turned out to be promising
Planning under uncertainty solving largescale stochastic linear programs(
)
2 editions published in 1992 in English and held by 0 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
2 editions published in 1992 in English and held by 0 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
Algorithmic advances in stochastic programming by
Stanford University(
)
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
Practical planning problems with deterministic forecasts of inherently uncertain parameters often yield unsatisfactory solutions. Stochastic programming formulations allow uncertain parameters to be modeled as random variables with known distributions, but the size of the resulting mathematical programs can be formidable. Decompositionbased algorithms take advantage of special structure and provide an attractive approach to such problems. We consider two classes of decompositionbased stochastic programming algorithms. The first type of algorithm addresses problems with a ''manageable'' number of scenarios. The second class incorporates Monte Carlo sampling within a decomposition algorithm. We develop and empirically study an enhanced Benders decomposition algorithm for solving multistage stochastic linear programs within a prespecified tolerance. The enhancements include warm start basis selection, preliminary cut generation, the multicut procedure, and decision tree traversing strategies. Computational results are presented for a collection of ''realworld'' multistage stochastic hydroelectric scheduling problems. Recently, there has been an increased focus on decompositionbased algorithms that use sampling within the optimization framework. These approaches hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. With this as motivation, we develop a stopping rule theory for algorithms in which bounds on the optimal objective function value are estimated by sampling. Rules are provided for selecting sample sizes and terminating the algorithm under which asymptotic validity of confidence interval statements for the quality of the proposed solution can be verified. Issues associated with the application of this theory to two samplingbased algorithms are considered, and preliminary empirical coverage results are presented
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
Practical planning problems with deterministic forecasts of inherently uncertain parameters often yield unsatisfactory solutions. Stochastic programming formulations allow uncertain parameters to be modeled as random variables with known distributions, but the size of the resulting mathematical programs can be formidable. Decompositionbased algorithms take advantage of special structure and provide an attractive approach to such problems. We consider two classes of decompositionbased stochastic programming algorithms. The first type of algorithm addresses problems with a ''manageable'' number of scenarios. The second class incorporates Monte Carlo sampling within a decomposition algorithm. We develop and empirically study an enhanced Benders decomposition algorithm for solving multistage stochastic linear programs within a prespecified tolerance. The enhancements include warm start basis selection, preliminary cut generation, the multicut procedure, and decision tree traversing strategies. Computational results are presented for a collection of ''realworld'' multistage stochastic hydroelectric scheduling problems. Recently, there has been an increased focus on decompositionbased algorithms that use sampling within the optimization framework. These approaches hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. With this as motivation, we develop a stopping rule theory for algorithms in which bounds on the optimal objective function value are estimated by sampling. Rules are provided for selecting sample sizes and terminating the algorithm under which asymptotic validity of confidence interval statements for the quality of the proposed solution can be verified. Issues associated with the application of this theory to two samplingbased algorithms are considered, and preliminary empirical coverage results are presented
A discountedcost continuoustime flexible manufacturing and operator scheduling model solved by deconvexification over time by
B. Curtis Eaves(
)
1 edition published in 1990 in English and held by 0 WorldCat member libraries worldwide
A discountedcost, continuoustime, infinitehorizon version of a flexible manufacturing and operator scheduling model is solved. The solution procedure is to convexify the discrete operatorassignment constraints to obtain a linear program, and then to regain the discreteness and obtain an approximate manufacturing schedule by deconvexification of the solution of the linear program over time. The strong features of the model are the accommodation of linear inequality relations among the manufacturing activities and the discrete manufacturing scheduling, whereas the weak features are intraperiod relaxation of inventory availability constraints, and the absence of inventory costs, setup times, and setup charges
1 edition published in 1990 in English and held by 0 WorldCat member libraries worldwide
A discountedcost, continuoustime, infinitehorizon version of a flexible manufacturing and operator scheduling model is solved. The solution procedure is to convexify the discrete operatorassignment constraints to obtain a linear program, and then to regain the discreteness and obtain an approximate manufacturing schedule by deconvexification of the solution of the linear program over time. The strong features of the model are the accommodation of linear inequality relations among the manufacturing activities and the discrete manufacturing scheduling, whereas the weak features are intraperiod relaxation of inventory availability constraints, and the absence of inventory costs, setup times, and setup charges
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Related Identities
 Electric Power Research Institute Sponsor
 United States Department of Energy Oakland Operations Office Researcher
 United States Department of Energy Office of Scientific and Technical Information Distributor
 Dantzig, George B. (George Bernard) 19142005 Author Editor
 National Science Foundation (U.S.) Sponsor
 Cottle, Richard Author
 Connolly, Thomas J. 1923
 Gill, Philip E. Author
 United States Department of Defense Sponsor
 United States Department of Energy Sponsor
Associated Subjects
Energy policyEconomic aspects Flexible manufacturing systems Industrial water supplyMathematical models Laminated wood Linear complementarity problem Linear programming Matrices Nonlinear programming Nonlinear programmingData processing Operations research Parallel processing (Electronic computers) Power resourcesMathematical models Production scheduling Programming (Mathematics) Simplexes (Mathematics) United States Water resources developmentMathematical models WatersupplyMathematical models
Alternative Names
S.O.L.
S.O.L. (Stanford University. Systems Optimization Laboratory)
SOL
SOL (Stanford University. Systems Optimization Laboratory)
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
Systems Optimization Laboratory
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