Related papers: Global Optimization on an Evolving Energy Landscap…
The paper considers a distributed algorithm for global minimization of a nonconvex function. The algorithm is a first-order consensus + innovations type algorithm that incorporates decaying additive Gaussian noise for annealing, converging…
An efficient machine-learning-based method combined with a conventional local optimization technique has been proposed for exploring local energy minima of interstitial species in a crystal. In the proposed method, an effective initial…
Particles interacting with short-ranged potentials have attracted increasing interest, partly for their ability to model mesoscale systems such as colloids interacting via DNA or depletion. We consider the free energy landscape of such…
The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This gives inside into the complexity of the energy…
Global optimization, particularly for non-convex functions with multiple local minima, poses significant challenges for traditional gradient-based methods. While metaheuristic approaches offer empirical effectiveness, they often lack…
Finding the optimal solution to a complex optimization problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be…
An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior,…
Molecular dynamics simulations are used to generate an ensemble of saddles of the potential energy of a Lennard-Jones liquid. Classifying all extrema by their potential energy u and number of unstable directions k, a well defined relation…
Preparing low energy states is a central challenge in quantum computing and quantum complexity theory. Several known approaches to prepare low energy states often get stuck in suboptimal states, such as high energy eigenstates (or low…
We present a genetic algorithm developed (GA) to optimize molecular AF_6 cluster configurations with respect to their energy. The method is based on the Darvin's evolutionary theory: structures with lowest energies survive in a system of…
Recent advances have shown that the circuit simulation algorithms that allow for solving highly nonlinear circuits of over one billion variables can be applicable to power system simulation and optimization problems through the use of an…
Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…
We consider a modification of the OMM energy functional which contains an $\ell^1$ penalty term in order to find a sparse representation of the low-lying eigenspace of self-adjoint operators. We analyze the local minima of the modified…
The structure of pipe networks minimizing the total energy dissipation rate is studied analytically. Among all the possible pipe networks that can be built with a given total pipe volume (or pipe lateral surface area), the network which…
We numerically study the potential energy landscape of a fragile glassy system and find that the dynamic crossover corresponding to the glass transition is actually the effect of an underlying geometric transition caused by a qualitative…
Disconnectivity graphs are used to visualize the minima and the lowest energy barriers between the minima of complex systems. They give an easy and intuitive understanding of the underlying energy landscape and, as such, are excellent tools…
Global Optimization with First-principles Energy Expressions (GOFEE) is an efficient method for identifying low energy structures in computationally expensive energy landscapes such as the ones described by density functional theory (DFT),…
We develop lower bounds for the energy of configurations in $\mathbb{R}^d$ periodic with respect to a lattice. In certain cases, the construction of sharp bounds can be formulated as a finite dimensional, multivariate polynomial…
We present a simple mathematical model of glassy dynamics seen as a random walk in a directed, weighted network of minima taken as a representation of the energy landscape. Our approach gives a broader perspective to previous studies…
We give noise-robust, Probably Approximately Correct (PAC) guarantees of global $\varepsilon$-optimality for the Variational Quantum Eigensolver under explicit geometric conditions. For periodic ansatzes with bounded generators -- yielding…