最优化与控制
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
It is quite often claimed, and correctly so, that linear methods cannot achieve global stability results for attitude control, and conversely that nonlinear control is essential in order to achieve (almost) globally stable tracking of…
We study a hierarchical federated learning (FL) problem, where clients cooperatively seek to select among multiple optimal solutions of a primary distributed learning problem, a solution that minimizes a secondary loss function. This…
The computation of the dominant eigenpair for symmetric positive semidefinite matrices is fundamental in numerical optimization. This work shifts the paradigm from the classical Rayleigh quotient to an unconstrained difference formulation,…
We study integral-to-integral input-to-state stability for infinite-dimensional linear systems with inputs and trajectories in $L^p$-spaces. We start by developing the corresponding admissibility theory for linear systems with unbounded…
We consider the optimization problem with a generally quadratic matrix constraint of the form $X^TAX = J$, where $A$ is a given nonsingular, symmetric $n\times n$ matrix and $J$ is a given $k\times k$ symmetric matrix, with $k\leq n$,…
Bregman proximal-type algorithms (BPs), such as mirror descent, have become popular tools in machine learning and data science for exploiting problem structures through non-Euclidean geometries. In this paper, we show that BPs can get…
Feedback optimization enables autonomous optimality seeking of a dynamical system through its closed-loop interconnection with iterative optimization algorithms. Among various iteration structures, model-based approaches require the…
In this work, we consider bilevel optimization when the lower-level problem is strongly convex. Recent works show that with a Hessian-vector product (HVP) oracle, one can provably find an $\epsilon$-stationary point within…
We introduce MathOptInterface, an abstract data structure for representing mathematical optimization problems based on combining pre-defined functions and sets. MathOptInterface is significantly more general than existing data structures in…
In industrial scenarios involving multi-agent collective decision-making, centralized decision-making may not be admissible due to restrictive access to individual local information, while the conflicts between participants' self-interest…
Modern optimal control theory involves adjoining the already known equations of motion of a dynamic system to the objective function using dynamic costates; this is done in order to constrain the optimal control solutions to satisfy the…
We study the solution of symmetric positive-definite linear systems by way of families of full- and limited-memory methods. Our contributions are threefold. We first derive new relationships between the conjugate-gradient method (CG) and…
This paper introduces a framework for Chance-Constrained Optimization with Complex Variables, addressing complex linear programming for both individual and joint probabilistic constraints in the complex domain. We first analyze the 3CP…
The moment-sum-of-squares hierarchy provides a powerful framework for solving non-convex optimal control problems by constructing a sequence of convex semidefinite relaxations. However, when extending these methods to nonlinear partial…
In scheduling problems, deterministic task durations are often assumed. This usually does not capture reality and may lead to schedules that are not robust to (small) changes to these task lengths. The use of stochastic task durations…
Real-time hierarchical energy-sharing markets are promising to coordinate large numbers of prosumers. Still, most existing clearing methods rely on linearized or DC power-flow models and do not explicitly handle reactive power or…
This paper investigates the optimal transport problem within the framework of Linear Quadratic optimal control systems. We establish the well-posedness of the Monge problem and analyze the regularity of the resulting optimal transport map,…
This paper addresses the generation expansion planning (GEP) problem, formulated as a mixed-integer linear programming model with intertemporal storage constraints. Being generally NP-hard, the problem's computational complexity grows…
We propose a framework for suboptimal model predictive control (MPC) based on the interconnection of monotone dynamical systems, such as port-Hamiltonian systems. In contrast to classical MPC formulations, where the optimizer is treated as…