相关论文: A Successive Gap Constraint Linearization Method f…
Mathematical programs with complementarity constraints are notoriously difficult to solve due to their nonconvexity and lack of constraint qualifications in every feasible point. This work focuses on the subclass of quadratic programs with…
In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…
LP relaxation-based message passing algorithms provide an effective tool for MAP inference over Probabilistic Graphical Models. However, different LP relaxations often have different objective functions and variables of differing…
While techniques have been developed for chance constrained stochastic optimal control using sample disturbance data that provide a probabilistic confidence bound for chance constraint satisfaction, far less is known about how to use sample…
We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of {\em subset selection}…
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…
It is well established that formulating an effective constraint model of a problem of interest is crucial to the efficiency with which it can subsequently be solved. Following from the observation that it is difficult, if not impossible, to…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state…
In this workshop, we discuss several algorithms for mathematical programs with equilibrium constraints (MPECs). The unifying theme is that MPECs are optimization problems whose feasible set contains a lower-level equilibrium system, often…
The alternating-current optimal power flow (ACOPF) is one of the best known non-convex non-linear optimisation problems. We present a novel re-formulation of ACOPF, which is based on lifting the rectangular power-voltage rank-constrained…
We investigate optimal control problems with $L^0$ constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation…
We present an optimisation-based method for synthesising a dynamic regret optimal controller for linear systems with potentially adversarial disturbances and known or adversarial initial conditions. The dynamic regret is defined as the…
This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of…
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…
In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…
Dynamical systems with a distributed yet interconnected structure, like multi-rigid-body robots or large-scale multi-agent systems, introduce valuable sparsity into the system dynamics that can be exploited in an optimal control setting for…
We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying…
A notion of $L^p$-exact controllability is introduced for linear controlled (forward) stochastic differential equations, for which several sufficient conditions are established. Further, it is proved that the $L^p$-exact controllability,…
This paper presents a Successive Convexification ($ \texttt{SCvx} $) algorithm to solve a class of non-convex optimal control problems with certain types of state constraints. Sources of non-convexity may include nonlinear dynamics and…