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Book Source: Digital Library of India Item 2015.191679 dc.contributor.author: M.l.malik dc.date.accessioned: 2015-07-08T01:08:11Z dc.date.available: 2015-07-08T01:08:11Z dc.date.digitalpublicationdate: 2005-08-20 dc.identifier.barcode: 1990010090175 dc.identifier.origpath: /rawdataupload/upload/0090/175 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/191679 dc.description.scannerno: 12 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 112 dc.format.mimetype: application/pdf dc.language.iso: English dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.subject.classification: Electrical Engineering dc.title: Linear And Nonlinear Programming On Analog Computer

viii, 250 p. : 24 cm

viii, 250 p. : 24 cm

Several algorithms in linear and nonlinear programming have been developed and analyzed. A worst-case analysis of the steepest edge simplex method showed it to have exponential time-complexity. This algorithm was specialized for solving minimum cost network flow problems and a partial pricing variant was developed. After extensive testing on randomly generated large problems the method was found to be inferior to efficiently coded partial pricing variants of the 'standard' simplex method except for the max flow problem and the problem of finding a feasible flow. On the max flow problem the algorithm was compared with the Edmonds-Karp and Dinic algorithms and found to be superior. In quadratic programming, the use of the steepest edge (face) criterion for dropping constraints was found to be helpful. Dual methods were found to be even more efficient and their use in recursive quadratic programming algorithms for nonlinear programming problems is recommended. A numerically stable ellipsoid algorithm for linear programming was developed and analyzed. At present the main promise that this method holds is as a powerful theoretical tool. Several minimization algorithms for taking advantage of negative curvature were developed as was a curvilinear steplength algorithm which ensures convergence to a positive semidefinite point. (Author)

Several algorithms in linear and nonlinear programming have been developed and analyzed. A worst-case analysis of the steepest edge simplex method showed it to have exponential time-complexity. This algorithm was specialized for solving minimum cost network flow problems and a partial pricing variant was developed. After extensive testing on randomly generated large problems the method was found to be inferior to efficiently coded partial pricing variants of the 'standard' simplex method except for the max flow problem and the problem of finding a feasible flow. On the max flow problem the algorithm was compared with the Edmonds-Karp and Dinic algorithms and found to be superior. In quadratic programming, the use of the steepest edge (face) criterion for dropping constraints was found to be helpful. Dual methods were found to be even more efficient and their use in recursive quadratic programming algorithms for nonlinear programming problems is recommended. A numerically stable ellipsoid algorithm for linear programming was developed and analyzed. At present the main promise that this method holds is as a powerful theoretical tool. Several minimization algorithms for taking advantage of negative curvature were developed as was a curvilinear steplength algorithm which ensures convergence to a positive semidefinite point. (Author)

A new method is given for preventing the simplex method from cycling. Key features are that a positive step is taken at every iteration, and nonbasic variables are allowed to be slightly infeasible. There is no additional work per iteration. Computational results are given for the first 53 test problems in netlib, indicating reliable performance in all cases. The method may be applied to active-set methods for solving nonlinear programs with linear constraints. Keywords: EXPAND procedure, EXPAND(Expanding Tolerance Anti-Degeneracy), Optimization.

A new method is given for preventing the simplex method from cycling. Key features are that a positive step is taken at every iteration, and nonbasic variables are allowed to be slightly infeasible. There is no additional work per iteration. Computational results are given for the first 53 test problems in netlib, indicating reliable performance in all cases. The method may be applied to active-set methods for solving nonlinear programs with linear constraints. Keywords: EXPAND procedure, EXPAND(Expanding Tolerance Anti-Degeneracy), Optimization.

A new method is given for preventing the simplex method from cycling. Key features are that a positive step is taken at every iteration, and nonbasic variables are allowed to be slightly infeasible. There is no additional work per iteration. Computational results are given for the first 53 test problems in netlib, indicating reliable performance in all cases. The method may be applied to active-set methods for solving nonlinear programs with linear constraints. Keywords: EXPAND procedure, EXPAND(Expanding Tolerance Anti-Degeneracy), Optimization.

A new method is given for preventing the simplex method from cycling. Key features are that a positive step is taken at every iteration, and nonbasic variables are allowed to be slightly infeasible. There is no additional work per iteration. Computational results are given for the first 53 test problems in netlib, indicating reliable performance in all cases. The method may be applied to active-set methods for solving nonlinear programs with linear constraints. Keywords: EXPAND procedure, EXPAND(Expanding Tolerance Anti-Degeneracy), Optimization.

Linear and Nonlinear Programming by David G.Luenberger and Yinyu Ye

The project explored the theoretical properties and computational performance of algorithms for solving constrained optimization problems (linear and nonlinear programs). Particular emphasis was placed on algorithms for solving large problems. The practical applications of optimization are innumerable. For example, mathematical models of the economy (to analyze the optimal use of natural resources) are typically large linear or nonlinear programs. Areas in which we have been actively involved include optimal generation and transmission of electricity, optimization of aircraft and spacecraft trajectories, optimal structural design, and financial modeling such as portfolio optimization. Progress on solution algorithms and software for such applications is ultimately reflected in improved techniques in many other areas of science and industry.

The project explored the theoretical properties and computational performance of algorithms for solving constrained optimization problems (linear and nonlinear programs). Particular emphasis was placed on algorithms for solving large problems. The practical applications of optimization are innumerable. For example, mathematical models of the economy (to analyze the optimal use of natural resources) are typically large linear or nonlinear programs. Areas in which we have been actively involved include optimal generation and transmission of electricity, optimization of aircraft and spacecraft trajectories, optimal structural design, and financial modeling such as portfolio optimization. Progress on solution algorithms and software for such applications is ultimately reflected in improved techniques in many other areas of science and industry.

Book Source: Digital Library of India Item 2015.192686 dc.contributor.author: M.l.malik dc.date.accessioned: 2015-07-08T01:32:06Z dc.date.available: 2015-07-08T01:32:06Z dc.date.digitalpublicationdate: 2005-08-20 dc.identifier.barcode: 1990010091087 dc.identifier.origpath: /rawdataupload/upload/0091/087 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/192686 dc.description.scannerno: 12 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 112 dc.format.mimetype: application/pdf dc.language.iso: English dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.subject.classification: Electrical Engineering dc.title: Linear And Nonlinear Programming On Analog Computer

The paper discusses duality for linear and nonlinear programs in which some of the variables are arbitrarily constrained. The most important class of such problems is that of mixed-integer (linear and nonlinear) programs. The paper introduces the duality constructions and discusses algorithms based on them.

The project involves study of the theoretical properties and computational performance of techniques that solve linear and nonlinear programs by means of nonlinear transformations. The group at the Systems Optimization Laboratory (SOL) were the first to recognize the connection between Karmarkar's (1984) projective method and the logarithmetic barrier method (see Gill, Murray, Saunders, Tomlin and Wright, 1986). It is now generally recognized that essentially all interior-point methods for linear programming inspired by Karmarkar's method are closely related to application of Newton's method to a sequence of barrier functions (see e.g., Gonzaga, 1987; Renegar, 1988, Anstreicher, 1988). Each barrier function is defined from the objective function and a barrier term that is infinite along the boundary of the feasible region. As the weight on the barrier term is reduced to zero, the solution of the subproblem becomes closer to the solution of the original problem.

This document is chiefly a bibliography listing titles such as: An Efficient Interactive Solution Framework for Bicriteria Integer Programming, An Improved Interactive Multicriteria Integer Programming Algorithm, An Interactive Multicriteria Linear Programming Method Using Constraints and Convex Cones.

Since Griffith and Stewart firstly proposed as successive linear programming method for solving general nonlinear programming problems, such methods have been widely used in practice because of their ease of implementation and their ability to deal with large scale problems. However, neither the original version, nor a more recent one contain convergence proofs possibly because of non-robustness of their algorithms. Using exact penalty functions and Levenberg Marquardtlike steps, an improved algorithm has been recently devised. In this paper, we give this modified SLP method a theoretical analysis and covergence proof, and thereby provide a sound basis for it. (Author)

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general problem that lie in an optimal basis for the associated linear program. Gomory has shown how to solve the special knapsack problem by adapting a dynamic programming recursion originally designed for the ordinary knapsack problem, and has identified sufficient conditions under which the solution of the special knapsack problem will satisfy the nonnegativity requirements in the general integer program, thereby yielding an optimal solution to that problem as well. In this paper the author presents an algorithm for solving the special knapsack problem that is capable of accommodating a variety of constraints in addition to the special knapsack constraint. The purpose in doing this is to expand the range of problems for which the optimal solution for the special problem will also provide an optimal solution to the general integer program from which it was derived.

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general problem that lie in an optimal basis for the associated linear program. Gomory has shown how to solve the special knapsack problem by adapting a dynamic programming recursion originally designed for the ordinary knapsack problem, and has identified sufficient conditions under which the solution of the special knapsack problem will satisfy the nonnegativity requirements in the general integer program, thereby yielding an optimal solution to that problem as well. In this paper the author presents an algorithm for solving the special knapsack problem that is capable of accommodating a variety of constraints in addition to the special knapsack constraint. The purpose in doing this is to expand the range of problems for which the optimal solution for the special problem will also provide an optimal solution to the general integer program from which it was derived.

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general problem that lie in an optimal basis for the associated linear program. Gomory has shown how to solve the special knapsack problem by adapting a dynamic programming recursion originally designed for the ordinary knapsack problem, and has identified sufficient conditions under which the solution of the special knapsack problem will satisfy the nonnegativity requirements in the general integer program, thereby yielding an optimal solution to that problem as well. In this paper the author presents an algorithm for solving the special knapsack problem that is capable of accommodating a variety of constraints in addition to the special knapsack constraint. The purpose in doing this is to expand the range of problems for which the optimal solution for the special problem will also provide an optimal solution to the general integer program from which it was derived.

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general problem that lie in an optimal basis for the associated linear program. Gomory has shown how to solve the special knapsack problem by adapting a dynamic programming recursion originally designed for the ordinary knapsack problem, and has identified sufficient conditions under which the solution of the special knapsack problem will satisfy the nonnegativity requirements in the general integer program, thereby yielding an optimal solution to that problem as well. In this paper the author presents an algorithm for solving the special knapsack problem that is capable of accommodating a variety of constraints in addition to the special knapsack constraint. The purpose in doing this is to expand the range of problems for which the optimal solution for the special problem will also provide an optimal solution to the general integer program from which it was derived.

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general problem that lie in an optimal basis for the associated linear program. Gomory has shown how to solve the special knapsack problem by adapting a dynamic programming recursion originally designed for the ordinary knapsack problem, and has identified sufficient conditions under which the solution of the special knapsack problem will satisfy the nonnegativity requirements in the general integer program, thereby yielding an optimal solution to that problem as well. In this paper the author presents an algorithm for solving the special knapsack problem that is capable of accommodating a variety of constraints in addition to the special knapsack constraint. The purpose in doing this is to expand the range of problems for which the optimal solution for the special problem will also provide an optimal solution to the general integer program from which it was derived.