Related papers: Hybrid optimal control with mixed-integer Lagrangi…
Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…
In this manuscript, we present a comprehensive theoretical and numerical framework for the control of production-destruction differential systems. The general finite horizon optimal control problem is formulated and addressed through the…
We present a powerful and easy-to-implement algorithm for solving constrained optimization problems that involve $L_1$/total-variation regularization terms, and both equality and inequality constraints. We discuss the relationship of our…
In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The…
This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…
We introduce a modeling framework for manipulation planning based on the formulation of the dynamics as a projected dynamical system. This method uses implicit signed distance functions and their gradients to formulate an equivalent…
Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming-based methods and metaheuristic approaches, are two highly successful streams for…
We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction…
The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The…
Model predictive control offers a powerful framework for managing constrained systems, but its repeated online optimization can become computationally prohibitive. Multiparametric programming addresses this challenge by precomputing optimal…
Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is…
Space mission planning and spacecraft design are tightly coupled and need to be considered together for optimal performance; however, this integrated optimization problem results in a large-scale Mixed-Integer Nonlinear Programming (MINLP)…
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…
This work advances the maximum hands-off sparse control framework by developing a robust counterpart for constrained linear systems with parametric uncertainties. The resulting optimal control problem minimizes an $L^{0}$ objective subject…
Optimal control problems are crucial in various domains, including path planning, robotics, and humanoid control, demonstrating their broad applicability. The connection between optimal control and Hamilton-Jacobi (HJ) partial differential…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates…