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Designing high-performance electric machines that maintain their efficiency and reliability under uncertain material and operating conditions is crucial for industrial applications. In this paper, we present a novel framework for robust…
We shed light on the structure of the "three-operator" version of the forward-Douglas--Rachford splitting algorithm for finding a zero of a sum of maximally monotone operators $A + B + C$, where $B$ is cocoercive, involving only the…
Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
The problems of optimal recovery of unbounded operators are studied. Optimality means the highest possible accuracy and the minimal amount of discrete information involved. It is established that the truncation method, when certain…
We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…
This article presents a robust control strategy using Time-Optimal Model Predictive Control (TOMPC) for a two-level quantum system subject to bounded uncertainties. In this method, the control field is optimized over a finite horizon using…
Sum-of-squares (SOS) optimization provides a computationally tractable framework for certifying polynomial nonnegativity. If the considered problem is convex, the SOS problem can be transcribed into and solved by semi-definite programs.…
In this article we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The proposed…
Robust control is a core approach for controlling systems with performance guarantees that are robust to modeling error, and is widely used in real-world systems. However, current robust control approaches can only handle small system…
This paper considers the problem of real-time mode scheduling in linear time-varying switched systems subject to a quadratic cost functional. The execution time of hybrid control algorithms is often prohibitive for real-time applications…
Distributionally robust optimal control (DROC) is gaining interest. This study presents a reformulation method for discrete DROC (DDROC) problems to design optimal control policies under a worst-case distributional uncertainty. The…
We present algorithms for checking and enforcing robustness of concurrent programs against the Total Store Ordering (TSO) memory model. A program is robust if all its TSO computations correspond to computations under the Sequential…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…
Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions. Convergence rate estimates for these algorithms have received…
The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very…
Optimal contribution selection (OCS) is a selective breeding method that manages the conversion of genetic variation into genetic gain to facilitate short-term competitiveness and long-term sustainability in breeding programmes. Traditional…
The paper studies decentralized optimization over networks, where agents minimize a sum of {\it locally} smooth (strongly) convex losses and plus a nonsmooth convex extended value term. We propose decentralized methods wherein agents {\it…
We propose and analyze a versatile and general algorithm called nonlinear forward-backward splitting (NOFOB). The algorithm consists of two steps; first an evaluation of a nonlinear forward-backward map followed by a relaxed projection onto…
Optimization-based (OB) alternatives to traditional flux limiters couch preservation of properties such as local bounds and maximum principles into optimization problems, which impose these properties through inequality constraints. In this…