13,238 research outputs found
Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization
This paper proposes an algorithmic framework for solving parametric
optimization problems which we call adjoint-based predictor-corrector
sequential convex programming. After presenting the algorithm, we prove a
contraction estimate that guarantees the tracking performance of the algorithm.
Two variants of this algorithm are investigated. The first one can be used to
solve nonlinear programming problems while the second variant is aimed to treat
online parametric nonlinear programming problems. The local convergence of
these variants is proved. An application to a large-scale benchmark problem
that originates from nonlinear model predictive control of a hydro power plant
is implemented to examine the performance of the algorithms.Comment: This manuscript consists of 25 pages and 7 figure
Robust Region-of-Attraction Estimation
We propose a method to compute invariant subsets of the region-of-attraction for asymptotically stable equilibrium points of polynomial dynamical systems with bounded parametric uncertainty. Parameter-independent Lyapunov functions are used to characterize invariant subsets of the robust region-of-attraction. A branch-and-bound type refinement procedure reduces the conservatism. We demonstrate the method on an example from the literature and uncertain controlled short-period aircraft dynamics
Reinforcement Learning Based on Real-Time Iteration NMPC
Reinforcement Learning (RL) has proven a stunning ability to learn optimal
policies from data without any prior knowledge on the process. The main
drawback of RL is that it is typically very difficult to guarantee stability
and safety. On the other hand, Nonlinear Model Predictive Control (NMPC) is an
advanced model-based control technique which does guarantee safety and
stability, but only yields optimality for the nominal model. Therefore, it has
been recently proposed to use NMPC as a function approximator within RL. While
the ability of this approach to yield good performance has been demonstrated,
the main drawback hindering its applicability is related to the computational
burden of NMPC, which has to be solved to full convergence. In practice,
however, computationally efficient algorithms such as the Real-Time Iteration
(RTI) scheme are deployed in order to return an approximate NMPC solution in
very short time. In this paper we bridge this gap by extending the existing
theoretical framework to also cover RL based on RTI NMPC. We demonstrate the
effectiveness of this new RL approach with a nontrivial example modeling a
challenging nonlinear system subject to stochastic perturbations with the
objective of optimizing an economic cost.Comment: accepted for the IFAC World Congress 202
Particle algorithms for optimization on binary spaces
We discuss a unified approach to stochastic optimization of pseudo-Boolean
objective functions based on particle methods, including the cross-entropy
method and simulated annealing as special cases. We point out the need for
auxiliary sampling distributions, that is parametric families on binary spaces,
which are able to reproduce complex dependency structures, and illustrate their
usefulness in our numerical experiments. We provide numerical evidence that
particle-driven optimization algorithms based on parametric families yield
superior results on strongly multi-modal optimization problems while local
search heuristics outperform them on easier problems
A Method to Guarantee Local Convergence for Sequential Quadratic Programming with Poor Hessian Approximation
Sequential Quadratic Programming (SQP) is a powerful class of algorithms for
solving nonlinear optimization problems. Local convergence of SQP algorithms is
guaranteed when the Hessian approximation used in each Quadratic Programming
subproblem is close to the true Hessian. However, a good Hessian approximation
can be expensive to compute. Low cost Hessian approximations only guarantee
local convergence under some assumptions, which are not always satisfied in
practice. To address this problem, this paper proposes a simple method to
guarantee local convergence for SQP with poor Hessian approximation. The
effectiveness of the proposed algorithm is demonstrated in a numerical example
Multiplier-continuation algorthms for constrained optimization
Several path following algorithms based on the combination of three smooth penalty functions, the quadratic penalty for equality constraints and the quadratic loss and log barrier for inequality constraints, their modern counterparts, augmented Lagrangian or multiplier methods, sequential quadratic programming, and predictor-corrector continuation are described. In the first phase of this methodology, one minimizes the unconstrained or linearly constrained penalty function or augmented Lagrangian. A homotopy path generated from the functions is then followed to optimality using efficient predictor-corrector continuation methods. The continuation steps are asymptotic to those taken by sequential quadratic programming which can be used in the final steps. Numerical test results show the method to be efficient, robust, and a competitive alternative to sequential quadratic programming
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