Computational Mathematical ProgrammingKarla L. Hoffman, Richard Henry Frymuth Jackson, J. Telgen As modelling efforts attempt to solve problems related to ever more complex systems, and as algorithms are developed specifically to handle problems having thousands (or even hundreds of thousands) of variables, the need for sound computational testing and full disclosure of experimental results is both obvious and immediate. This collection of papers reflects both the current technology available to mathematical programmers for solving optimization problems, and mechanisms for testing and determining the quality of software used. This testing requires suitable test problems and the execution of a designed experiment to determine the efficiency, robustness, reliability and applicability of various algorithms. Many aspects of computational mathematical programming are covered: the testing of new algorithms for optimizing functions of a specified form, computational comparisons of known algorithms, a preliminary computational evaluation of the new projective method, why decomposition methods have not been as successful as originally anticipated, etc. |
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Contents
PREFACE | 1 |
R S DEMBO A primal truncated Newton algorithm with application | 43 |
FLÅM Approximating some convex programs in terms of Borel fields | 73 |
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active constraints active set ALRQP1 analysis augmented Lagrangian bits of precision bound column complementary solution convergence convex defined Dembo denote descent direction electrical network error evaluations extreme point feasibility tolerances feasible point finite function and gradient gradient values GRG2 Hatfield Hatfield Polytechnic Hessian implementation inequality initial Lagrange multipliers large-scale LCNLP line search linear complementarity problem linear programming LSM1 master problem Mathematical Programming matrix minimum MINOS NLPNET node non-zeros nonbasic variables nonlinear network nonlinear programming number of iterations objective function obtain path penalty function penalty parameter performance pivots positive definite procedure programming problems projective PTN algorithm quadratic approximation quadratic programming reduced gradient relaxing direction relaxing step REQP restricted Schittkowski search direction Section simplex method simplicial decomposition solving sparse matrix strategy structure subproblem superbasic Table test problems truncated-Newton trust region update vector W₁ है है है