Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well conditioned problems. In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for problems of this class. Computational experience … Read more
An iterative procedure to find the optimal solutions of general fractional nonlinear delay systems with quadraticperformance indices is introduced. The derivatives of state equations are understood in the Caputo sense. By presenting and applying a general framework, we use the Chebyshev wavelet method developed for fractional linear optimal control to convert fractional nonlinear optimal control … Read more
This paper focuses on the development of decentralized collaborative sensing and sensor resource allocation algorithms where the sensors are located on-board autonomous unmanned aerial vehicles. We develop these algorithms in the context of single-target and multi-target tracking applications, where the objective is to maximize the tracking performance as measured by the mean-squared error between the … Read more
Knowledge-based determination of the best-possible experimental setups for nanoparticle design is highly challenging. Additionally, such processes are accompanied by noticeable uncertainties. Therefore, protection against these uncertainties is needed. Robust optimization helps determining such best possible processes. The latter guarantees quality requirements regardless of how the uncertainties, e.g. with regard to variations in raw materials, heat … Read more
We can compress a neural network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable. However, current approaches to determine the stability of neurons in networks with Rectified Linear Unit (ReLU) activations require solving or finding a good approximation to multiple discrete optimization problems. … Read more
We describe a finite-horizon partially observable Markov decision process (POMDP) approach to optimize decisions about whether and when to perform biopsies for patients on active surveillance for prostate cancer. The objective is to minimize a weighted combination of two criteria, the number of biopsies to conduct over a patient’s lifetime and the delay in detecting … Read more
In this paper we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. The symbolic regression problem can be formulated as … Read more
Renewable energy and modernization of power operation demand Independent System Operators (ISOs) to solve ever more complex and larger programming problems to securely and economically schedule power resources. A key step in the scheduling process is the unit commitment (UC). In a hydro-dominated system, this process also involves managing reservoirs and is called hydrothermal UC … Read more
In this paper, we present a decentralized unmanned aerial vehicle (UAV) swarm formation control approach based on a decision theoretic approach. Specifically, we pose the UAV swarm motion control problem as a decentralized Markov decision process (Dec-MDP). Here, the goal is to drive the UAV swarm from an initial geographical region to another geographical region … Read more
It is well-known that simple short-sighted algorithms, such as gradient descent, generalize well in the over-parameterized learning tasks, due to their implicit regularization. However, it is unknown whether the implicit regularization of these algorithms can be extended to robust learning tasks, where a subset of samples may be grossly corrupted with noise. In this work, … Read more