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We propose a solution approach for the problem (P) of minimizing an unconstrained binary polynomial optimization problem. We call this method PQCR (Polynomial Quadratic Convex Reformulation). The resolution is based on a 3-phase method. The…
We propose the use of controlled perturbations to address the challenging question of optimal active-set prediction for interior point methods. Namely, in the context of linear programming, we consider perturbing the inequality…
We consider nonlinear model predictive control (MPC) with multiple competing cost functions. In each step of the scheme, a multiobjective optimal control problem with a nonlinear system and terminal conditions is solved. We propose an…
Model Predictive Control (MPC) can efficiently control constrained systems in real-time applications. MPC feedback law for a linear system with linear inequality constraints can be explicitly computed off-line, which results in an off-line…
Mixed-Integer Quadratically Constrained Quadratic Programs arise in a variety of applications, particularly in energy, water, and gas systems, where discrete decisions interact with nonconvex quadratic constraints. These problems are…
Faster, cheaper, and more power efficient optimization solvers than those currently offered by general-purpose solutions are required for extending the use of model predictive control (MPC) to resource-constrained embedded platforms. We…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
This paper investigates adaptive model predictive control (MPC) for a class of constrained linear systems with unknown model parameters. This is also posed as the dual control problem consisting of system identification and regulation. We…
Symmetry is the essential element of lifted inference that has recently demon- strated the possibility to perform very efficient inference in highly-connected, but symmetric probabilistic models models. This raises the question, whether…
We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…
Model Predictive Control (MPC) has become a popular framework in embedded control for high-performance autonomous systems. However, to achieve good control performance using MPC, an accurate dynamics model is key. To maintain real-time…
This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying…
We consider a parametric convex quadratic programming, CQP, relaxation for the quadratic knapsack problem, QKP. This relaxation maintains partial quadratic information from the original QKP by perturbing the objective function to obtain a…
Determining the evolutionary history of a given biological data is an important task in biological sciences. Given a set of quartet topologies over a set of taxa, the Maximum Quartet Consistency (MQC) problem consists of computing a global…
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…
Classical control of cyber-physical systems used to rely on basic linear controllers. These controllers provided a safe and robust behavior but lack the ability to perform more complex controls such as aggressive maneuvering or performing…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
We propose a data-driven Model Predictive Control (MPC) framework that employs a transformer encoder to generate multi-step predictions. To handle the nonconvex attention mechanism, we derive difference of convex (DC) representations of the…
Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This…
In this paper, we address the problem of reducing the computational burden of Model Predictive Control (MPC) for real-time robotic applications. We propose TransformerMPC, a method that enhances the computational efficiency of MPC…