Related papers: A Dynamical Systems Perspective on Discrete Optimi…
Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of…
A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order…
Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for…
Many combinatorial optimization problems can be mapped to finding the ground states of the corresponding Ising Hamiltonians. The physical systems that can solve optimization problems in this way, namely Ising machines, have been attracting…
Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous…
The Ising model provides a natural mapping for many computationally hard combinatorial optimization problems (COPs). Consequently, dynamical system-inspired computing models and hardware platforms that minimize the Ising Hamiltonian, have…
The equivalence between the natural minimization of energy in a dynamical system and the minimization of an objective function characterizing a combinatorial optimization problem offers a promising approach to designing dynamical…
We present a new way to make Ising machines, i.e., using networks of coupled self-sustaining nonlinear oscillators. Our scheme is theoretically rooted in a novel result that establishes that the phase dynamics of coupled oscillator systems,…
In this paper, we report new results on a novel Ising machine technology for solving combinatorial optimization problems using networks of coupled self-sustaining oscillators. Specifically, we present several working hardware prototypes…
Many combinatorial optimization problems can be reformulated as finding the ground state of the Ising model. Existing Ising solvers are mostly inspired by simulated annealing. Although annealing techniques offer scalability, they lack…
Combinatorial optimization problems can be mapped onto Ising models, and their ground state is generally difficult to find. A lot of heuristics for these problems have been proposed, and one promising approach is to use continuous…
Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
Reconfigurable intelligent surfaces (RISs) are often assumed to allow continuous phase control over all elements, leading to hardware cost that scales with the number of elements. Treating the phase of each element as a discrete variable is…
Dynamical Ising machines are based on continuous dynamical systems evolving from a generic initial state to a state strongly related to the ground state of the classical Ising model on a graph. Reaching the ground state is equivalent to…
The rich non-linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While…
We develop an optimization framework centered around a core idea: once a (parametric) policy is specified, control authority is transferred to the policy, resulting in an autonomous dynamical system. Thus we should be able to optimize…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
Oscillator Ising Machines (OIMs) and probabilistic bit (p-bit)-based computing platforms have emerged as promising paradigms for tackling complex combinatorial optimization problems. Although traditionally viewed as distinct approaches,…