4,347 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
Optimal mistuning for enhanced aeroelastic stability of transonic fans
An inverse design procedure was developed for the design of a mistuned rotor. The design requirements are that the stability margin of the eigenvalues of the aeroelastic system be greater than or equal to some minimum stability margin, and that the mass added to each blade be positive. The objective was to achieve these requirements with a minimal amount of mistuning. Hence, the problem was posed as a constrained optimization problem. The constrained minimization problem was solved by the technique of mathematical programming via augmented Lagrangians. The unconstrained minimization phase of this technique was solved by the variable metric method. The bladed disk was modelled as being composed of a rigid disk mounted on a rigid shaft. Each of the blades were modelled with a single tosional degree of freedom
SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0)
SDPNAL+ is a {\sc Matlab} software package that implements an augmented
Lagrangian based method to solve large scale semidefinite programming problems
with bound constraints. The implementation was initially based on a majorized
semismooth Newton-CG augmented Lagrangian method, here we designed it within an
inexact symmetric Gauss-Seidel based semi-proximal ADMM/ALM (alternating
direction method of multipliers/augmented Lagrangian method) framework for the
purpose of deriving simpler stopping conditions and closing the gap between the
practical implementation of the algorithm and the theoretical algorithm. The
basic code is written in {\sc Matlab}, but some subroutines in C language are
incorporated via Mex files. We also design a convenient interface for users to
input their SDP models into the solver. Numerous problems arising from
combinatorial optimization and binary integer quadratic programming problems
have been tested to evaluate the performance of the solver. Extensive numerical
experiments conducted in [Yang, Sun, and Toh, Mathematical Programming
Computation, 7 (2015), pp. 331--366] show that the proposed method is quite
efficient and robust, in that it is able to solve 98.9\% of the 745 test
instances of SDP problems arising from various applications to the accuracy of
in the relative KKT residual
- …