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We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of…
This paper delves into the challenging issues in uncertain multi-objective optimization, where uncertainty permeates nonsmooth nonconvex objective and constraint functions. In this context, we investigate highly robust (weakly efficient)…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…
A robust positioning pattern is a large array that allows a mobile device to locate its position by reading a possibly corrupted small window around it. In this paper, we provide constructions of binary positioning patterns, equipped with…
This paper studies the robust optimal control design for uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (robust-ADP). The objective is to fill up a gap in the past literature of ADP where dynamic…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
In this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that…
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
Motion planning is a fundamental problem and focuses on finding control inputs that enable a robot to reach a goal region while safely avoiding obstacles. However, in many situations, the state of the system may not be known but only…
This paper studies the problem of optimal investment in incomplete markets, robust with respect to stopping times. We work on a Brownian motion framework and the stopping times are adapted to the Brownian filtration. Robustness can only be…
We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An $(a,b)$-supermatch is a stable matching in which if $a$ pairs break up it is possible to find another stable…
An approximate formulation of a robust geometric program (RGP) as a convex program is proposed. Interest in using geometric programs (GPs) to model complex engineering systems has been growing, and this has motivated explicitly modeling the…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
This paper proposes a new logic RoCTL* to model robustness in concurrent systems. RoCTL* extends CTL* with the addition of Obligatory and Robustly operators, which quantify over failure-free paths and paths with one more failure…
We consider the following problem: Given a rational matrix $A \in \setQ^{m \times n}$ and a rational polyhedron $Q \subseteq\setR^{m+p}$, decide if for all vectors $b \in \setR^m$, for which there exists an integral $z \in \setZ^p$ such…
We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the competitive condition and transversality condition being unconditionally sufficient for…