Related papers: Inner-Approximating Reachable Sets for Polynomial …

The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…

This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all…

Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…

This paper combines two ingredients in order to get a rather surprising result on one of the most studied, elegant and powerful tools for solving convex feasibility problems, the method of alternating projections (MAP). Going back to names…

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…

We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…

We study the complexity of identifying the integer feasibility of reverse convex sets. We present various settings where the complexity can be either NP-Hard or efficiently solvable when the dimension is fixed. Of particular interest is the…

For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…

In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulation proposed in our previous work and the quadratic modules…

This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T…

In this paper, we propose an iterative algorithm to address the nonconvex multi-group multicast beamforming problem with quality-of-service constraints and per-antenna power constraints. We formulate a convex relaxation of the problem as a…

We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and…

This paper tackles the challenging problem of finding global optimal solutions for two-stage stochastic programs with continuous decision variables and nonconvex recourse functions. We introduce a two-phase approach. The first phase…

Determining the reachable set for a given nonlinear system is critically important for autonomous trajectory planning for reach-avoid applications and safety critical scenarios. Providing the reachable set is generally impossible when the…

We give a full characterization of the range of the operator which associates, to any initial condition, the viscosity solution at time $T$ of a Hamilton-Jacobi equation with convex Hamiltonian. Our main motivation is to be able to treat…

We study the problem of finding the Lowner-John ellipsoid, i.e., an ellipsoid with minimum volume that contains a given convex set. We reformulate the problem as a generalized copositive program, and use that reformulation to derive…

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…

For hybrid systems exhibiting periodic behavior, analyzing the invariant set containing the limit cycle is a natural way to study the robustness of the closed-loop system. However, computing these sets can be computationally expensive,…

Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…

This paper addresses a fundamental challenge in data-driven reachability analysis: accurately representing and propagating non-convex reachable sets. We propose a novel approach using constrained polynomial zonotopes to describe reachable…