相关论文: Global Optimization on an Evolving Energy Landscap…

Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N-1)- dimensional sphere is one of the simplest, yet paradigmatic problems in Optimization Theory known as the "trust…

We propose an extended genetic algorithm (GA) with different local environmental conditions. Genetic entities, or configurations, are put on nodes in a ring structure, and location-dependent environmental conditions are applied for each…

We prove localization and probabilistic bounds on the minimum level spacing for a random block Anderson model without monotonicity. Using a sequence of narrowing energy windows and associated Schur complements, we obtain detailed…

Intermittent renewable energy resources like wind and solar pose great uncertainty of multiple time scales, from minutes to years, on the design and operation of power systems. Energy system optimization models have been developed to find…

When applying optimization method to a real-world problem, the possession of prior knowledge and preliminary analysis on the landscape of a global optimization problem can give us an insight into the complexity of the problem. This…

We provide a general framework for the optimal design of surface energies on networks. We prove sharp bounds for the homogenization of discrete systems describing mixtures of ferromagnetic interactions by constructing optimal…

We conducted a comprehensive numerical investigation of the energy landscape of the Thomson problem for systems up to $N=150$. Our results show the number of distinct configurations grows exponentially with $N$, but significantly faster…

Global changes of states are of crucial importance in optimization algorithms. We review some heuristic algorithms in which global updates are realized by a sort of real-space renormalization group transformation. Emphasis is on the…

We consider the global minimization of a particular type of minimum structured optimization problems wherein the variables must belong to some basic set, the feasible domain is described by the intersection of a large number of functional…

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…

One of the most useful methods for studying the stable homotopy category is localising at some spectrum E. For an arbitrary stable model category we introduce a candidate for the E-localisation of this model category. We study the…

The downward continuation of potential fields from the Earth's surface into the subsurface is a critical task in gravity exploration, as it helps to identify the sources of gravity anomalies. This problem is often addressed by solving a…

Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…

Adopting a zonal structure of electricity market requires specification of zones' borders. One of the approaches to identify zones is based on clustering of Locational Marginal Prices (LMP). The purpose of the paper is twofold: (i) we…

The influence of quadrupolar interactions on the structure of small clusters is investigated by adding a point quadrupole of variable strength to the Lennard-Jones potential. Competition arises between sheet-like arrangements of the…

We study global minimizers of a functional modeling the free energy of thin liquid layers over a solid substrate under the combined effect of surface, gravitational, and intermolecular potentials. When the latter ones have a mild repulsive…

We consider the problem of minimizing the supplied energy of infinite-dimensional linear port-Hamiltonian systems and prove that optimal trajectories exhibit the turnpike phenomenon towards certain subspaces induced by the dissipation of…

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…

We present an efficient algorithm for calculating the minimum energy path (MEP) and energy barriers between local minima on a multidimensional potential energy surface (PES). Such paths play a central role in the understanding of transition…

We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a…