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In this paper we design and analyze algorithms for asynchronously solving linear programs using nonlinear signal processing structures. In particular, we discuss a general procedure for generating these structures such that a fixed-point of…
We study the computational complexity of decision problems in $k$-level linear programming (LP). Seminal work by Jeroslow establishes that determining whether the optimal objective value of a $k$-level LP is at least as good as a given…
The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible…
We present a novel prompt design for Large Language Models (LLMs) tailored to Asynchronous Time Series. Unlike regular time series, which assume values at evenly spaced time points, asynchronous time series consist of timestamped events…
In this study, we present a deep learning-optimization framework to tackle dynamic mixed-integer programs. Specifically, we develop a bidirectional Long Short Term Memory (LSTM) framework that can process information forward and backward in…
We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…
Factor-revealing linear programs (LPs) and policy-revealing LPs arise in various contexts of algorithm design and analysis. They are commonly used techniques for analyzing the performance of approximation and online algorithms, especially…
In this paper, we address the problem of time-optimal coordination of mobile robots under kinodynamic constraints along specified paths. We propose a novel approach based on time discretization that leads to a mixed-integer linear…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
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…
Finding an optimal decision tree that minimizes classification error is known to be NP-hard. While exact algorithms based on MILP, CP, SAT, or dynamic programming guarantee optimality, they often suffer from poor anytime behavior -- meaning…
This paper discusses the odds problem, proposed by Bruss in 2000, and its variants. A recurrence relation called a dynamic programming (DP) equation is used to find an optimal stopping policy of the odds problem and its variants. In 2013,…
Fast and accurate large-scale energy system models are needed to investigate the potential of storage to complement the fluctuating energy production of renewable energy systems. However, standard Mixed-Integer Programming (MIP) models that…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
The aims of this article are two-fold. First, we give a geometric characterization of the optimal basic solutions of the general linear programming problem (no compactness assumptions) and provide a simple, self-contained proof of it…
We propose a Fully Polynomial-Time Approximation Scheme (FPTAS) for stochastic dynamic programs with multidimensional action, scalar state, convex costs and linear state transition function. The action spaces are polyhedral and described by…
High-dimensional nonlinear optimization problems subject to nonlinear constraints can appear in several contexts including constrained physical and dynamical systems, statistical estimation, and other numerical models. Feasible optimization…
Maximal parabolic $L^p$-regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity on a fixed surface. By freezing the coefficients…
This paper introduces a novel approach to evaluating the asymptotic stability of equilibrium points in both continuous-time (CT) and discrete-time (DT) nonlinear autonomous systems. By utilizing indirect Lyapunov methods and linearizing…