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Second-order Newton-type algorithms that leverage the exact Hessian or its approximation are central to solve nonlinear optimization problems. However, their applications in solving large-scale nonconvex problems are hindered by three…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
We find an exact mapping from the generalized Ising models with many-spin interactions to equivalent Boltzmann machines, i.e., the models with only two-spin interactions between physical and auxiliary binary variables accompanied by local…
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…
Ising Machine is a promising computing approach for solving combinatorial optimization problems. It is naturally suited for energy-saving and compact in-memory computing implementations with emerging memories. A na\"ive in-memory computing…
We present a heuristic algorithm designed to solve Quadratic Unconstrained Binary Optimization (QUBO) problems efficiently. The algorithm, referred to as IC-D2S, leverages a hybrid approach using Ising and classical machines to address very…
We study the performance scaling of three quantum algorithms for combinatorial optimization: measurement-feedback coherent Ising machines (MFB-CIM), discrete adiabatic quantum computation (DAQC), and the D\"urr-Hoyer algorithm for quantum…
A coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs), in which the "strongest" collective mode of oscillation at well above threshold corresponds to an optimum solution of a given Ising problem. When a pump…
While the Ising model remains essential to understand physical phenomena, its natural connection to combinatorial reasoning makes it also one of the best models to probe complex systems in science and engineering. We bring a computational…
We consider a spacecraft formation reconfiguration problem in the case of identical spacecraft. This introduces in the optimal reconfiguration problem a permutational degree of freedom, in addition to the choice of individual spacecraft…
We propose an efficient method to compute a small set of integer-constrained cone singularities, which induce a rotationally seamless conformal parameterization with low distortion. Since the problem only involves discrete variables, i.e.,…
Combinatorial optimization problems (COPs) are crucial in many applications but are computationally demanding. Traditional Ising annealers address COPs by directly converting them into Ising models (known as direct-E transformation) and…
We investigate the information complexity of mixed-integer convex optimization under different types of oracles. We establish new lower bounds for the standard first-order oracle, improving upon the previous best known lower bound. This…
In recent years, hardware implementations of Ising machines have emerged as a viable alternative to quantum computing for solving hard optimization problems among other applications. Unlike quantum hardware, dense connectivity can be…
In this paper we present a reformulation--framed as a constrained optimization problem--of multi-robot tasks which are encoded through a cost function that is to be minimized. The advantages of this approach are multiple. The…
We analyze the bootstrap approach (a dual optimization method to the variational approach) to one-dimensional spin chains, leveraging semidefinite programming to extract numerical results. We study how correlation functions in the ground…
Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions from the plasma and the external sources, are best formulated…
Markov Chain Monte Carlo (MCMC) underlies both statistical physics and combinatorial optimization, but mixes slowly near critical points and in rough landscapes. Parallel Tempering (PT) improves mixing by swapping replicas across…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…