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Decomposition methods in optimization
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application approximations assumed Barnsley Barnsley Area behavioural models brachistochrone problem calculations calculus of variations chapter coal preparation coal preparation plants coefficients column Complete Master Problem complex conjugate gradient consider control theory convergence cost function decentralized decision model decomposition denoted derivatives described differential equation discussed drawdown dual coordination dynamic dynamic programming economic estimated Euler equation evaluation example feeder given Hence hierarchy implemented important increase inequality constraints input iteration Lagrange multipliers Lagrangian line searches linear programming mathematical programming matrix maximize maximum demand minimize minimum nonlinear Nonlinear Programming objective function objective value on-line optimal solution optimization problem output overfitting parameters possible preparation plant primal procedures quasi-Newton methods refill reservoir runoff satisfy simplex algorithm solve step stochastic strategy structure subproblem subsystem techniques telecommunications Theorem trajectory unconstrained users variables vector