A detailed analysis of convergence rate is presented for an iterative path formulated optimal routing algorithm. In particular, it is quantified, analytically, how the convergence rate changes as the number of nodes i...
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A detailed analysis of convergence rate is presented for an iterative path formulated optimal routing algorithm. In particular, it is quantified, analytically, how the convergence rate changes as the number of nodes in the underlying graph increases. The analysis is motivated by a particular path formulated gradient projection algorithm that has demonstrated excellent convergence rate properties through extensive numerical studies. The analytical result proven in this note is that the number of iterations for convergence depends on the number of nodes only through the network diameter.
This paper describes an algorithm for optimization of a smooth function subject to general linear constraints. An algorithm of the gradientprojection class is used, with the important feature that the "projectio...
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This paper describes an algorithm for optimization of a smooth function subject to general linear constraints. An algorithm of the gradientprojection class is used, with the important feature that the "projection" at each iteration is performed by using a primal-dual interior-point method for convex quadratic programming. Convergence properties can be maintained even if the projection is done inexactly in a well-defined way. Higher-order derivative information on the manifold defined by the apparently active constraints can be used to increase the rate of local convergence.
A gradient projection algorithm is presented for the dynamic dispatch of thermal generations, based upon an active set strategy and exploiting second order information in determining the descent directions. The algori...
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A gradient projection algorithm is presented for the dynamic dispatch of thermal generations, based upon an active set strategy and exploiting second order information in determining the descent directions. The algorithm is adapted to the model of the dynamic dispatch problem which consists of the minimisation of a nonlinear objective function subject to quadratic equality constraints and linear inequality constraints. The envisaged algorithm can be applied to the dispatching of thermal units during the steep load pick-up and drop-down periods over short time intervals, and can also be used in the day-before scheduling after the unit commitment has been performed. Efficiency is demonstrated by tests on large-scale networks representative of the Italian EHV system. The limited CPU time requirements also suggest a possible on-line application in determining the constrained participation factors to be used in the Automatic Generation Control function.
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