Lisandro A. Parente

A Class of Inexact Variable Metric Proximal Point Algorithms

For the problem of solving maximal monotone inclusions, we present a rather general class of algorithms, which contains hybrid inexact proximal point methods as a special case and allows for the use of a variable metric in subproblems. The global convergence and local linear rate of convergence are established under standard assumptions. We demonstrate the advantage of variable metric implementation in the case of solving systems of smooth monotone equations by the proximal Newton method.

Stabilization of the Generalized Benders Decomposition applied to Short-Term Hydrothermal Coordination Problem

Solving the Short Term Hydrothermal Coordination (STHTC) Problem considers the resolution of both the Unit Commitment (UC) and the Economic Dispatch (ED) for thermal and hydraulic units. In order to avoid post-dispatch corrections, the transmission network is modeled with a high level of detail considering an AC power flow. These facts lead to a very complex optimization problem which is solved by using a novel decomposition approach which combines Generalized Benders Decomposition (GBD) with Bundle methods presented in [LS97]. This proposed method resembles a stabilized version of the cutting planes method, which drastically reduces the well-known tailing-off effect that Benders methods have. The approach presented in this work allows the decomposition of the whole problem in a quadratic mixed integer master problem, and in a non-linear subproblem which should be separable. The former defines the state and the active power dispatched by each unit whereas the latter determines the reactive power to meet the electrical constraints through a modified AC optimal power flow (OPF). These approaches were applied to a 9-bus test case, and to the IEEE 24-bus test case. The problem is solved for a time horizon of a day with a one-hour step.

Solving minimax control problems via nonsmooth optimization

We address minimax optimal control problems with linear dynamics. Under convexity assumptions, by using non-smooth optimization techniques, we derive a set of optimality conditions for the continuous-time case. We define an approximated discrete-time problem where analogous conditions hold. One of them allows us to design an easily implementable descent method. We analyze its convergence and we show some preliminary numerical results.

Fully discrete schemes for monotone optimal control problems

In this article, we study an infinite horizon optimal control problem with monotone controls. We analyze the associated Hamilton–Jacobi–Bellman (HJB) variational inequality which characterizes the value function and consider the totally discretized problem using Lagrange elements to approximate the state space

Discrete time schemes for optimal control problems with monotone controls

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The Demand Adjustment Problem via Inexact Restoration Method.

Ω. The convergence orders of these approximations are proved, which are in general

Solving net constrained hydrothermal Nash-Cournot equilibrium problems via the proximal decomposition method

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