Related papers: Using non-convex approximations for efficient anal…
In this manuscript, we propose a general proximal quasi-Newton method tailored for nonconvex and nonsmooth optimization problems, where we do not require the sequence of the variable metric (or Hessian approximation) to be uniformly bounded…
This papers studies multi-agent (convex and \emph{nonconvex}) optimization over static digraphs. We propose a general distributed \emph{asynchronous} algorithmic framework whereby i) agents can update their local variables as well as…
Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…
In this paper, a novel approach is introduced which utilizes a Rapidly-exploring Random Graph to improve sampling-based autonomous exploration of unknown environments with unmanned ground vehicles compared to the current state of the art.…
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…
The maximum hands-off control is the optimal solution to the L0 optimal control problem. It has the minimum support length among all feasible control inputs. To avoid computational difficulties arising from its combinatorial nature, the…
In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically…
The first part of this paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In…
The quadratic system provided by the Time of Arrival technique can be solved analytically or by optimization algorithms. In practice, a combination of both methods is used. An important problem in quadratic optimization is the possible…
Boolean programs with multiple recursive threads can be captured as pushdown automata with multiple stacks. This model is Turing complete, and hence, one is often interested in analyzing a restricted class that still captures useful…
In this paper, a convex optimization-based method is proposed for numerically solving dynamic programs in continuous state and action spaces. The key idea is to approximate the output of the Bellman operator at a particular state by the…
Motivated by TRACE algorithm [Curtis et al. 2017], we propose a trust region algorithm for finding second order stationary points of a linearly constrained non-convex optimization problem. We show the convergence of the proposed algorithm…
A practical challenge for structural estimation is the requirement to accurately minimize a sample objective function which is often non-smooth, non-convex, or both. This paper proposes a simple algorithm designed to find accurate solutions…
Many optimization algorithms$\unicode{x2013}$including gradient descent, proximal methods, and operator splitting techniques$\unicode{x2013}$can be formulated as fixed-point iterations (FPI) of continuous operators. When these operators are…
We focus on decentralized stochastic non-convex optimization, where $n$ agents work together to optimize a composite objective function which is a sum of a smooth term and a non-smooth convex term. To solve this problem, we propose two…
Non-convex optimization problems can be approximately solved via relaxation or local algorithms. For many practical problems such as optimal power flow (OPF) problems, both approaches tend to succeed in the sense that relaxation is usually…
Given a simple polygon $\cal P$, in the Art Gallery problem the goal is to find the minimum number of guards needed to cover the entire $\cal P$, where a guard is a point and can see another point $q$ when $\overline{pq}$ does not cross the…
We present a new technique for demonstrating the reachability of states in deterministic finite automata representing the concatenation of two languages. Such demonstrations are a necessary step in establishing the state complexity of the…
In this paper we introduce and study a class of structured set-valued operators which we call union averaged nonexpansive. At each point in their domain, the value of such an operator can be expressed as a finite union of single-valued…
Model predictive control allows solving complex control tasks with control and state constraints. However, an optimal control problem must be solved in real-time to predict the future system behavior, which is hardly possible on embedded…