10,396 research outputs found
An Alternating Trust Region Algorithm for Distributed Linearly Constrained Nonlinear Programs, Application to the AC Optimal Power Flow
A novel trust region method for solving linearly constrained nonlinear
programs is presented. The proposed technique is amenable to a distributed
implementation, as its salient ingredient is an alternating projected gradient
sweep in place of the Cauchy point computation. It is proven that the algorithm
yields a sequence that globally converges to a critical point. As a result of
some changes to the standard trust region method, namely a proximal
regularisation of the trust region subproblem, it is shown that the local
convergence rate is linear with an arbitrarily small ratio. Thus, convergence
is locally almost superlinear, under standard regularity assumptions. The
proposed method is successfully applied to compute local solutions to
alternating current optimal power flow problems in transmission and
distribution networks. Moreover, the new mechanism for computing a Cauchy point
compares favourably against the standard projected search as for its activity
detection properties
The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning
In this paper we study the split minimization problem that consists of two
constrained minimization problems in two separate spaces that are connected via
a linear operator that maps one space into the other. To handle the data of
such a problem we develop a superiorization approach that can reach a feasible
point with reduced (not necessarily minimal) objective function values. The
superiorization methodology is based on interlacing the iterative steps of two
separate and independent iterative processes by perturbing the iterates of one
process according to the steps dictated by the other process. We include in our
developed method two novel elements. The first one is the permission to restart
the perturbations in the superiorized algorithm which results in a significant
acceleration and increases the computational efficiency. The second element is
the ability to independently superiorize subvectors. This caters to the needs
of real-world applications, as demonstrated here for a problem in
intensity-modulated radiation therapy treatment planning.Comment: Revised version, October 10, 2022; accepted for publication in:
Applied Mathematics and Computatio
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