Related papers: Minimum Cost Feedback Selection for Arbitrary Pole…
One often encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for controlled Markov chains. In this paper, we provide a method to construct sub-optimal policies along with a bound…
This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS)…
This paper addresses the problem of safe autonomous navigation in unknown obstacle-filled environments using only local sensory information. We propose a smooth feedback controller derived from an unconstrained penalty-based formulation…
This paper develops a sequential-linearization feedback optimization framework for driving nonlinear dynamical systems to an optimal steady state. A fundamental challenge in feedback optimization is the requirement of accurate first-order…
This paper addresses the problem of stabilization for infinite-dimensional systems. In particular, we design nonlinear stabilizers for both linear and nonlinear abstract systems. We focus on two classes of systems: the first class comprises…
We present a $\frac53$-approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2-edge connected spanning…
Feedback optimization refers to a class of methods that steer a control system to a steady state that solves an optimization problem. Despite tremendous progress on the topic, an important problem remains open: enforcing state constraints…
The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regev (2003) proved that the problem is NP-hard to approximate within a factor $2 - \epsilon$, assuming the Unique…
We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
We consider a wireless network with a set of transmitter-receiver pairs, or links, that share a common channel, and address the problem of emptying finite traffic volume from the transmitters in minimum time. This, so called, minimum-time…
We study the complexity of finding communication trees with the lowest possible completion time for rooted, irregular gather and scatter collective communication operations in fully connected, $k$-ported communication networks under a…
A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…
Partial set cover problem and set multi-cover problem are two generalizations of set cover problem. In this paper, we consider the partial set multi-cover problem which is a combination of them: given an element set $E$, a collection of…
The minimum feedback arc set problem asks to delete a minimum number of arcs (directed edges) from a digraph (directed graph) to make it free of any directed cycles. In this work we approach this fundamental cycle-constrained optimization…
In this study we consider the shortest path problem, where the arc costs are subject to distributional uncertainty. Basically, the decision-maker attempts to minimize her worst-case expected loss over an ambiguity set (or a family) of…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving…
We study the problems of covering or partitioning a polygon $P$ (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contained in an axis-aligned unit square. For covering, we seek to…
This paper proposes an optimization with penalty-based feedback design framework for safe stabilization of control affine systems. Our starting point is the availability of a control Lyapunov function (CLF) and a control barrier function…