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The V U -algorithm is a superlinearly convergent method for minimizing nonsmooth, convex functions. At each iteration, the algorithm works with a certain V -space and its orthogonal U -space, such that the nonsmoothness of the objective function is concentrated on its projection onto the V -space, and on the U -space the projection is smooth. This structure allows for an alternation between a Newton-like step where the function is smooth, and a proximal-point step that is used to find iterates with promising V U -decompositions. We establish a derivative-free variant of the V U -algorithm for convex finite-max objective functions. We show global convergence and provide numerical results from a proof-of-concept implementation, which demonstrates the feasibility and practical value of the approach. We also carry out some tests using nonconvex functions and discuss the results. [ABSTRACT FROM AUTHOR]

The mid-term operation planning of hydro-thermal power systems needs a large number of synthetic sequences to represent accurately stochastic streamflows. These sequences are generated by a periodic autoregressive model. If the number of synthetic sequences is too big, the optimization planning problem may be too difficult to solve. To select a small set of sequences representing the stochastic process well enough, this work employs two variants of the Scenario Optimal Reduction technique. The first variant applies such a technique at the last stage of a tree defined a priori for the whole planning horizon while the second variant combines a stage-wise reduction, preserving the periodic autoregressive structure, with resampling. Both approaches are assessed numerically on hydrological sequences generated for real configurations of the Brazilian power system. [ABSTRACT FROM AUTHOR]

For a maximal monotone operator T on a Hilbert space H and a closed subspace A of H , we consider the problem of finding ( x , y ? T ( x )) satisfying x ? A and y ? A ? . An equivalent formulation of this problem makes use of the partial inverse operator of Spingarn. The resulting generalized equation can be solved by using the proximal point algorithm. We consider instead the use of hybrid proximal methods. Hybrid methods use enlargements of operators, close in spirit to the concept of e-subdifferentials. We characterize the enlargement of the partial inverse operator in terms of the enlargement of T itself. We present a new algorithm of resolution that combines Spingarn and hybrid methods, we prove for this method global convergence only assuming existence of solutions and maximal monotonicity of T . We also show that, under standard assumptions, the method has a linear rate of convergence. For the important problem of finding a zero of a sum of maximal monotone operators T 1 , ..., T m , we present a highly parallelizable scheme. Finally, we derive a parallel bundle method for minimizing the sum of polyhedral functions. [ABSTRACT FROM AUTHOR]