817 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
A sequential semidefinite programming method and an application in passive reduced-order modeling
We consider the solution of nonlinear programs with nonlinear
semidefiniteness constraints. The need for an efficient exploitation of the
cone of positive semidefinite matrices makes the solution of such nonlinear
semidefinite programs more complicated than the solution of standard nonlinear
programs. In particular, a suitable symmetrization procedure needs to be chosen
for the linearization of the complementarity condition. The choice of the
symmetrization procedure can be shifted in a very natural way to certain linear
semidefinite subproblems, and can thus be reduced to a well-studied problem.
The resulting sequential semidefinite programming (SSP) method is a
generalization of the well-known SQP method for standard nonlinear programs. We
present a sensitivity result for nonlinear semidefinite programs, and then
based on this result, we give a self-contained proof of local quadratic
convergence of the SSP method. We also describe a class of nonlinear
semidefinite programs that arise in passive reduced-order modeling, and we
report results of some numerical experiments with the SSP method applied to
problems in that class
A Parametric Non-Convex Decomposition Algorithm for Real-Time and Distributed NMPC
A novel decomposition scheme to solve parametric non-convex programs as they
arise in Nonlinear Model Predictive Control (NMPC) is presented. It consists of
a fixed number of alternating proximal gradient steps and a dual update per
time step. Hence, the proposed approach is attractive in a real-time
distributed context. Assuming that the Nonlinear Program (NLP) is
semi-algebraic and that its critical points are strongly regular, contraction
of the sequence of primal-dual iterates is proven, implying stability of the
sub-optimality error, under some mild assumptions. Moreover, it is shown that
the performance of the optimality-tracking scheme can be enhanced via a
continuation technique. The efficacy of the proposed decomposition method is
demonstrated by solving a centralised NMPC problem to control a DC motor and a
distributed NMPC program for collaborative tracking of unicycles, both within a
real-time framework. Furthermore, an analysis of the sub-optimality error as a
function of the sampling period is proposed given a fixed computational power.Comment: 16 pages, 9 figure
Incorporating a four-dimensional filter line search method into an interior point framework
Here we incorporate a four-dimensional filter line search method
into an infeasible primal-dual interior point framework for
nonlinear programming. Each entry in the filter has four components
measuring dual feasibility, complementarity, primal feasibility and
optimality. Three measures arise directly from the first order
optimality conditions of the problem and the fourth is the objective
function, so that convergence to a stationary point that is a
minimizer is guaranteed. The primary assessment of the method has
been done with a well-known collection of small problems
Comparison of filter line search algorithms in the primal-dual barrier approach for nonlinear programming
In this paper, we present a new filter line search method based on
two measures that is integrated into the primal-dual barrier method
developed by Wachter and Biegler [Mathematical Programming 106
(2006), pp. 25--57] for nonlinear programming. One measure arises
directly from the first order optimality conditions of the problem
and the other is the barrier function. Primary assessment of the
method has been done with a well-known collection of problems and
compared with the solver IPOPT.Fundação para a Ciência e a Tecnologia (FCT
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