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Une méthode d’optimisation non linéaire en variables mixtes pour la conception de procédés. (A nonlinear optimization method in mixed variables for the design of processes). (French) Zbl 0656.90071

A mixed-integer programming method for solving large-scale nonlinearly constrained problems is presented in this paper. Assuming convexity for the problem the equivalence of the solution of the original problem with the solution of a finite sequence of mixed-integer linear problems, involving a finite number of constraints is first proved by using the principles of the generalized Benders decomposition method. Then we show that the convergence of the solutions of this problem sequence towards the solution of the original problem is reached when two integer solutions into the sequence are identical.
After a presentation of the logical steps of the algorithm, where a reduced gradient method and a mixed-integer linear programming procedure are implemented, two numerical examples are detailed. The first one is a mathematical problem involving nonlinear constraints. The second one, found in the literature, is related to the optimal design of a gas transportation network, and shows the capability of the procedure for solving large-scale problems derived from actual industrial cases.

MSC:

90C11 Mixed integer programming
65K05 Numerical mathematical programming methods
90B10 Deterministic network models in operations research
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