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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algorithm angular applied assume assumptions b₁ basic feasible solution basic variables basis matrix Benders c₁ choose column components computed Consider constraint set convex combination convex function convex program convex set cycle Dantzig Dantzig-Wolfe decomposition decomposition principle defined Df(x differentiable dual method equation extreme point finite number gradient hyperplane inequality infeasible initial integer integer program inverse iteration Lagrange multiplier Lagrangian linear program lower bound m₁ maximize minimize f(x minimum negative nonbasic Nonlinear Programming nonnegative objective function objective value obtained optimal solution optimality test P₁ partition pivot operation primal problem primal-dual procedure PROOF r₁ reduced problem relative cost factors requires restricted master program S₁ saddle point satisfied Section simplex algorithm simplex method simplex multipliers slack variables solved subgradients subject to minimize subproblem subset subsystem supporting hyperplane tableau Theorem upper bound V₁ vector x₁ y₁ yields zero