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We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose…

Distributed control algorithms are known to reduce overall computation time compared to centralized control algorithms. However, they can result in inconsistent solutions leading to the violation of safety-critical constraints. Inconsistent…

Many high dimensional optimization problems can be reformulated into a problem of finding theoptimal state path under an equivalent state space model setting. In this article, we present a general emulation strategy for developing a state…

In this paper, we present the Monte-Carlo Compressive Optimization algorithm, a new method to solve a combinatorial optimization problem that is assumed compressible. The method relies on random queries to the objective function in order to…

Numerical global optimization methods are often very time consuming and could not be applied for high-dimensional nonconvex/nonsmooth optimization problems. Due to the nonconvexity/nonsmoothness, directly solving the primal problems…

In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…

Combinatorial optimization problems are central to both practical applications and the development of optimization methods. While classical and quantum algorithms have been refined over decades, machine learning--assisted approaches are…

Many realistic decision-making problems in networked scenarios, such as formation control and collaborative task offloading, often involve complicatedly entangled local decisions, which, however, have not been sufficiently investigated yet.…

Parallel tempering is a generic Markov chain Monte Carlo sampling method which allows good mixing with multimodal target distributions, where conventional Metropolis-Hastings algorithms often fail. The mixing properties of the sampler…

In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…

Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods…

In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control.…

In this paper, we propose an inexact Augmented Lagrangian Method (ALM) for the optimization of convex and nonsmooth objective functions subject to linear equality constraints and box constraints where errors are due to fixed-point data. To…

Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…

In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid…

Adiabatic quantum computers, such as the quantum annealers commercialized by D-Wave Systems Inc., are routinely used to tackle combinatorial optimization problems. In this article, we show how to exploit them to accelerate equilibrium…

Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a…

Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…

The time parallel solution of optimality systems arising in PDE constraint optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the…

We apply a recently developed adaptive algorithm that systematically improves the efficiency of parallel tempering or replica exchange methods in the numerical simulation of small proteins. Feedback iterations allow us to identify an…