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Designing controllers to generate various trajectories has been studied for years, while recently, recovering an optimal controller from trajectories receives increasing attention. In this paper, we reveal that the inherent linear quadratic…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
It is a longstanding unsolved problem to characterize the optimal feedback controls for general linear quadratic optimal control problem of stochastic evolution equation with random coefficients. A solution to this problem is given in [21]…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and…
In this paper, we consider the problem of distributed optimal control of linear dynamical systems with a quadratic cost criterion. We study the case of output feedback control for two interconnected dynamical systems, and show that the…
This paper studies the inverse optimal control problem for continuous-time linear quadratic regulators over finite-time horizon, aiming to reconstruct the control, state, and terminal cost matrices in the objective function from observed…
We study a linear quadratic optimal control problem with stochastic coefficients and a terminal state constraint, which may be in force merely on a set with positive, but not necessarily full probability. Under such a partial terminal…
A proximal safeguarded augmented Lagrangian method for minimizing the difference of convex (DC) functions over a nonempty, closed and convex set with additional linear equality as well as convex inequality constraints is presented. Thereby,…
This paper develops and analyzes feedback-based online optimization methods to regulate the output of a linear time-invariant (LTI) dynamical system to the optimal solution of a time-varying convex optimization problem. The design of the…
A Deterministic affine quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the value function is…
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…
In model predictive control (MPC), the choice of cost-weighting matrices and designing the Hessian matrix directly affects the trade-off between rapid state regulation and minimizing the control effort. However, traditional MPC in quadratic…
We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…
In this article we address the issue of uniqueness for differential and algebraic operator Riccati equations, under a distinctive set of assumptions on their unbounded coefficients. The class of boundary control systems characterized by…
We investigate a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…
We consider Riemannian optimization problems with inequality and equality constraints and analyze a class of Riemannian interior point methods for solving them. The algorithm of interest consists of outer and inner iterations. We show that,…
For various typical cases and situations where the formulation results in an optimal control problem, the Linear Quadratic Regulator (LQR) approach and its variants continue to be highly attractive. In certain scenarios, it can happen that…
Inactive constraints do not contribute to the solution of an optimal control problem, but increase the problem size and burden the numerical computations. We present a novel strategy for handling inactive constraints efficiently by…
This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…