## Optimization Theory for Large SystemsImportant text examines most significant algorithms for optimizing large systems and clarifying relations between optimization procedures. Much data appear as charts and graphs and will be highly valuable to readers in selecting a method and estimating computer time and cost in problem-solving. Initial chapter on linear and nonlinear programming presents all necessary background for subjects covered in rest of book. Second chapter illustrates how large-scale mathematical programs arise from real-world problems. Appendixes. List of Symbols. |

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This book addresses mathematicians, economists, engineers generally all those interested in systems theory, cybernetics, economic, operational research and computer science.

The author presents in a clear style, concise and sober most important algorithms for optimization of large systems. Different methods are grouped into classes and presented logically attractive. It is the first time clarifies connections between different optimization algorithms.

An extensive bibliography.

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algorithm angular applied assume assumptions basic feasible solution basic solution basic variables basis matrix Benders choose column components computed Consider constraint set convex combination convex function convex program convex set coupling variables cycle Dantzig Dantzig-Wolfe decomposition decomposition principle defined differentiable dual feasible dual method dual simplex method elementary matrices enter the basis equation example extreme point finite number FlGURE given gradient hyperplane inequality infeasible initial integer inverse iteration Lagrange multiplier linear program lower bound Mathematical Programming maximize minimum negative Nonlinear Programming nonnegative objective function objective value obtained optimal solution original problem partition pivot operation positive primal problem primal-dual procedure PROOF reduced problem relative cost factors relaxation requires restricted master program saddle point satisfied Section shown in Figure simplex algorithm simplex method simplex multipliers slack slack variables subgradients subset subsystem supporting hyperplane tableau Theorem upper bound yields zero