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

Local quadratic convergence of polynomial-time interior-point methods for conic optimization problems

In this paper, we establish a local quadratic convergence of polynomial-time interior-point methods for general conic optimization problems. The main structural property used in our analysis is the logarithmic homogeneity of self-concordant barrier functions. We propose new path-following predictor-corrector schemes which work only in the dual space. They are based on an easily computable gradient proximity measure, which ensures an automatic transformation of the global linear rate of convergence to the local quadratic one under some mild assumptions. Our step-size procedure for the predictor step is related to the maximum step size (the one that takes us to the boundary). It appears that in order to obtain local superlinear convergence, we need to tighten the neighborhood of the central path proportionally to the current duality gapconic optimization problem, worst-case complexity analysis, self-concordant barriers, polynomial-time methods, predictor-corrector methods, local quadratic convergence

An interior-point and decomposition approach to multiple stage stochastic programming

There is no abstract of this report

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

An Improved Data Augmentation Scheme for Model Predictive Control Policy Approximation

This paper considers the problem of data generation for MPC policy approximation. Learning an approximate MPC policy from expert demonstrations requires a large data set consisting of optimal state-action pairs, sampled across the feasible state space. Yet, the key challenge of efficiently generating the training samples has not been studied widely. Recently, a sensitivity-based data augmentation framework for MPC policy approximation was proposed, where the parametric sensitivities are exploited to cheaply generate several additional samples from a single offline MPC computation. The error due to augmenting the training data set with inexact samples was shown to increase with the size of the neighborhood around each sample used for data augmentation. Building upon this work, this letter paper presents an improved data augmentation scheme based on predictor-corrector steps that enforces a user-defined level of accuracy, and shows that the error bound of the augmented samples are independent of the size of the neighborhood used for data augmentation

A complexity bound of a predictor-corrector smoothing method using CHKS-functions for monotone LCP

We propose a new smoothing method using CHKS-functions for solving linear complementarity problems. While the algorithm in [6] uses a quite large neighborhood, our algorithm generates a sequence in a relatively narrow neighborhood and employs predictor and corrector steps at each iteration. A complexity bound for the method is also provided under the assumption that the problem is monotone and has a feasibleinterior point. As a result, the bound can be improved compared to the one in [6].Includes bibliographical references (p. 16-17

EFFICIENT SIZING OF STRUCTURES UNDER STRESS CONSTRAINTS

<p>Optimisation algorithms used to automatically size structural members commonly involve stress constraints to avoid material failure. Therefore the cost of optimisation grows rapidly as the number of structural members is increased due to the corresponding increase in the number of constraints. In this work, an efficient method for large scale stress constrained structural sizing optimisation problems is proposed. A convex, separable, and scalable approximation for stress constraints which splits the approximation into a local fully stressed term and a global load distribution term is introduced. Predictor-corrector interior point method, an excellent option for large scale optimization problem, is chosen to solve the approximate subproblems. The core idea in this work is to achieve computational efficiency in the optimization procedure by avoiding the construction and the solution of the Schur complement system generated by the interior point method. Avoiding the Schur complement, and explicit sensitivity analysis, eliminates the high cost of solving stress constrained problems within the interior point optimisation. This is achieved using the preconditioned conjugate gradient method, and a new preconditioner is proposed specifically for stress constrained problems. The proposed method is applied to a number of beam sizing problems. Numerical results show that optimal complexity is achieved by the algorithm, the computational cost being linearly proportional to the number of sizing variables.</p

Convergence analysis of an Inexact Infeasible Interior Point method for Semidefinite Programming

In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima,Megiddo and Mizuno (A primal-dual infeasible-interior-point algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use of inexact search directions; i.e., the linear systems defining the search directions can be solved with an accuracy that increases as the solution is approached. A convergence analysis is carried out and the global convergence of the method is prove