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Global optimization is a challenging problem, with plenty of algorithms displaying empirical success, but scarce theoretical backing. In this work, we propose a new theoretical framework called Proximal Basin Hopping (PBH), carefully…
Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy…
Global optimization is an active area of research in atomistic simulations, and many algorithms have been proposed to date. A prominent example is basin hopping Monte Carlo, which performs a modified Metropolis Monte Carlo search to explore…
In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian…
We study the non-convex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. This model is motivated by applications in molecular microscopy and image processing, where each…
Building upon our earlier work of a martingale approach to global optimization, a powerful stochastic search scheme for the global optimum of cost functions is proposed on the basis of change of measures on the states that evolve as…
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal…
We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…
The relaxation of binary spins to analog values has been the subject of much debate in the field of statistical physics, neural networks, and more recently quantum computing, notably because the benefits of using an analog state for finding…
Power systems are globally experiencing an unprecedented growth in size and complexity due to the advent of nonconventional generation and consumption technologies. To navigate computational complexity, power system dynamic models are often…
We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian $H$. This is a central problem in physics with vast applications in many-body systems and…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…
We consider the problem of minimizing the sum of a smooth function $h$ with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function $P$ and a surjective linear map $\cal…
This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
In this paper, we build on recent work using a mathematical programming approach for incremental state update in analysis of non-linear mechanics models. In particular, we consider quasi-static analysis of continuum problems in the…
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
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…
By combining the continuous matrix product state (cMPS) representation for quantum fields in the continuum with standard optimization techniques for matrix product states (MPS) on the lattice, we obtain an approximation $|\Psi\rangle$,…
This paper presents a novel algorithm integrating global and robust optimization methods to solve continuous non-convex quadratic problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines…