## Decomposition Methods for Structured Convex Programming |

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Academic Computing Center active constraints add quadratic terms algorithm to solve back to Step Best-Ritter boundedness Chapter closed convex function constraints and variables CONVEX PROGRAMMING convex set corresponding coupling constraints coupling variables Dantzig-Wolfe decomposition decomposition method decomposition procedure decomposition technique defined design variables dual problem finite element FMPS-LP given inner minimization 4.12 Karush-Kuhn-Tucker conditions Lagrange multipliers large-scale LCPL linear programming problem Lipschitz continuously Madison Academic Computing matrix minimization problem modified algorithm objective function optimal solution original problem outer loop outer minimization P P P P polyhedron positive definite positive number prob problem 3.1 problem min 6(x problems with coupling proximal point algorithm proximal point method quadratic function quadratic programming problems Rockafellar sequence simplex method smaller subproblems solve the problem starting point storage requirements straints strongly convex subject to C.x. Subroutine Table test problems Thierauf tion UNIVAC University of Wisconsin-Madison vector yield conditions