Related papers: Nonanalyticity of the optimized effective potentia…
A description of non-collinear magnetism in the framework of spin-density functional theory is presented for the exact exchange energy functional which depends explicitly on two-component spinor orbitals. The equations for the effective…
To ensure preservation of local or global bounds for numerical solutions of conservation laws, we constrain a baseline finite element discretization using optimization-based (OB) flux correction. The main novelty of the proposed methodology…
We consider the problem of obtaining higher order in regularization parameter $\epsilon$ analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of differential equations and direct…
A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the…
The optimized effective potential method is formulated as a convex minimization problem. This formulation does not require assumptions about $v$-representability nor functional differentiability. The formulation provides a natural framework…
In Paper I, the effective one-electron potentials (OEP) method was introduced and demonstrated as an efficient approach to reduce the computational cost of evaluation of the charge-transfer interaction energy within the effective fragment…
We critically examine the applicability of the effective potential within dynamical situations and find, in short, that the answer is negative. An important caveat of the use of an effective potential in dynamical equations of motion is an…
We present a general methodology to evaluate matrix elements of the effective core potentials (ECPs) within one-electron basis set of Slater-type orbitals (STOs). The scheme is based on translation of individual STO distributions in the…
The optimized effective potential (OEP) method presents an unambiguous way to construct the Kohn-Sham potential corresponding to a given diagrammatic approximation for the exchange-correlation functional. The OEP from the random-phase…
The Performance Estimation Problem (PEP) approach consists in computing worst-case performance bounds on optimization algorithms by solving an optimization problem: one maximizes an error criterion over all initial conditions allowed and…
We have derived a new method which allows to compute the full and the Pauli reference kinetic potentials for atoms and molecules in a real space representation. This is done by applying the optimized effective potential (OEP) method to…
We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. The focus is on problems where one seeks to optimize the…
In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set…
We prove that a solution of an elliptic operator with periodic coefficients behaves on large scales like an analytic function, in the sense of approximation by polynomials with periodic corrections. Equivalently, the constants in the…
Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
The optimized effective potential equations for atoms have been solved by parameterizing the potential. The expansion is tailored to fulfill the known asymptotic behavior of the effective potential at both short and long distances. Both…
The EHP and the MCAP provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. Both approaches utilize the mixed formulation and lead to the development of…
Quality Diversity (QD) algorithms such as MAP-Elites are a class of optimisation techniques that attempt to find many high performing points that all behave differently according to a user-defined behavioural metric. In this paper we…