Related papers: Some notes on applying computational divided diffe…
It is well-known that proper scaling can increase the efficiency of computational problems. In this paper we define and show that a balancing technique can substantially improve the computational efficiency of optimal control algorithms. We…
Finite-precision arithmetic computations face an inherent tradeoff between accuracy and efficiency. The points in this tradeoff space are determined, among other factors, by different data types but also evaluation orders. To put it simply,…
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…
The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing…
Calculating the log-determinant of a matrix is useful for statistical computations used in machine learning, such as generative learning which uses the log-determinant of the covariance matrix to calculate the log-likelihood of model…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…
Computing Jacobians with automatic differentiation is ubiquitous in many scientific domains such as machine learning, computational fluid dynamics, robotics and finance. Even small savings in the number of computations or memory usage in…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact…
Finite difference (FD) approximation is a classic approach to stochastic gradient estimation when only noisy function realizations are available. In this paper, we first provide a sample-driven method via the bootstrap technique to estimate…
This paper proposes a distributed algorithm for a network of agents to solve an optimization problem with separable objective function and locally coupled constraints. Our strategy is based on reformulating the original constrained problem…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
A common approach for minimizing a smooth nonlinear function is to employ finite-difference approximations to the gradient. While this can be easily performed when no error is present within the function evaluations, when the function is…
The problem of differentiating a function with bounded second derivative in the presence of bounded measurement noise is considered in both continuous-time and sampled-data settings. Fundamental performance limitations of causal…
Recent studies have shown that fractional calculus is an effective alternative mathematical tool in various scientific fields. However, some investigations indicate that results established in differential and integral calculus do not…
There is a growing need for computational tools to automatically design and verify autonomous systems, especially complex robotic systems involving perception, planning, control, and hardware in the autonomy stack. Differentiable…
Differential computation (DC) is a highly general incremental computation/view maintenance technique that can maintain the output of an arbitrary and possibly recursive dataflow computation upon changes to its base inputs. As such, it is a…
We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the…