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A Global Optimization Method, αBB, for General TwiceDifferentiable Constrained NLPs: I  Theoretical Advances
, 1997
"... In this paper, the deterministic global optimization algorithm, αBB, (αbased Branch and Bound) is presented. This algorithm offers mathematical guarantees for convergence to a point arbitrarily close to the global minimum for the large class of twicedifferentiable NLPs. The key idea is the constru ..."
Abstract

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In this paper, the deterministic global optimization algorithm, αBB, (αbased Branch and Bound) is presented. This algorithm offers mathematical guarantees for convergence to a point arbitrarily close to the global minimum for the large class of twicedifferentiable NLPs. The key idea is the construction of a converging sequence of upper and lower bounds on the global minimum through the convex relaxation of the original problem. This relaxation is obtained by (i) replacing all nonconvex terms of special structure (i.e., bilinear, trilinear, fractional, fractional trilinear, univariate concave) with customized tight convex lower bounding functions and (ii) by utilizing some α parameters as defined by Maranas and Floudas (1994b) to generate valid convex underestimators for nonconvex terms of generic structure. In most cases, the calculation of appropriate values for the α parameters is a challenging task. A number of approaches are proposed, which rigorously generate a set of α par...
A Dual Algorithm for the Short Term Power Production Planning with Network Constraints
, 1998
"... We study an algorithm for the short term power production planning optimization problem, with network constraints. The system contains a set of generators which can be of different kinds, connected by a power transmission network. These need to be scheduled hourly, during a week time period. This is ..."
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We study an algorithm for the short term power production planning optimization problem, with network constraints. The system contains a set of generators which can be of different kinds, connected by a power transmission network. These need to be scheduled hourly, during a week time period. This is a complex problem, mainly due to the technical constraints of each generator, which include start up constraints for thermal units, and water flow constraints linking several hydro plants on the same river. The algorithm is based on a Lagrangian relaxation of a suitable set of coupling constraints, que permite resolver en forma separada los problemas de cada generador y los de la red de trasmision en cada paso de tiempo. The resulting dual problem is solved by means of a non differentiable convex optimization method, This algorithm has been tested with real data from the uruguayan system. Keywords: Short term power scheduling, hydro thermal coordination, unit commitement, large scale, netw...