Related papers: Structure-Exploiting Newton-Type Method for Optima…
We consider the problem of designing a machine learning-based model of an unknown dynamical system from a finite number of (state-input)-successor state data points, such that the model obtained is also suitable for optimal control design.…
The paper presents a novel method for designing an optimal controller for discrete-time switched linear systems. The problem is formulated as one of computing the discrete mode sequence and the continuous input sequence that jointly…
Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization problems or the Jacobian in system of nonlinear equations. In the Interior Point context,…
This paper presents a Newton-based stochastic extremum-seeking control method for real-time optimization in multi-input systems with distinct input delays. It combines predictor-based feedback and Hessian inverse estimation via stochastic…
Optimal control deals with optimization problems in which variables steer a dynamical system, and its outcome contributes to the objective function. Two classical approaches to solving these problems are Dynamic Programming and the…
In this paper, we study Newton-conjugate gradient (Newton-CG) methods for minimizing a nonconvex function $f$ whose Hessian is $(H_f,\nu)$-H\"older continuous with modulus $H_f>0$ and exponent $\nu\in(0,1]$. Recently proposed Newton-CG…
This paper introduces and analyses a continuous optimization approach to solve optimal control problems involving ordinary differential equations (ODEs) and tracking type objectives. Our aim is to determine control or input functions, and…
In this paper, we present an efficient semismooth Newton method, named SSNCP, for solving a class of semidefinite programming problems. Our approach is rooted in an equivalent semismooth system derived from the saddle point problem induced…
In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian…
Newton-type methods enjoy fast local convergence and strong empirical performance, but achieving global guarantees comparable to first-order methods remains challenging. Even for simple strongly convex problems, no straightforward variant…
We focus on finding sparse and least-$\ell_1$-norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, nevertheless recent versions of Newton method for under-determined…
This paper is concerned with the convergence of a two-step modified Newton method for solving the nonlinear system arising from the minimal nonnegative solution of nonsymmetric algebraic Riccati equations from neutron transport theory. We…
Differentiable optimal control, particularly differentiable nonlinear model predictive control (NMPC), provides a powerful framework that enjoys the complementary benefits of machine learning and control theory. A key enabler of…
In this article, we propose a Newton-based method for solving multiobjective interval optimization problems (MIOPs). We first provide a connection between weakly Pareto optimal points and Pareto critical points in the context of MIOPs.…
This paper investigates the optimal co-design of logical and continuous controls for switched linear systems governed by controlled logical switching dynamics. Unlike traditional switched systems with arbitrary or state-dependent switching,…
This paper considers the regularization continuation method and the trust-region updating strategy for the nonlinearly equality-constrained optimization problem. Namely, it uses the inverse of the regularization quasi-Newton matrix as the…
We consider online statistical inference of constrained stochastic nonlinear optimization problems. We apply the Stochastic Sequential Quadratic Programming (StoSQP) method to solve these problems, which can be regarded as applying…
Nonlinear Parametric Optimization Network (NLPOpt-Net) is an unsupervised learning architecture to solve constrained nonlinear programs (NLP). Given the structure of an NLP, it learns the parametric solution maps with guaranteed constraint…
In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these optimization problems efficiently and to have good upper bounds on worst-case…
The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical…