相关论文: Orbital optimization in the perfect pairing hierar…
Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To-date, experimental demonstrations of algorithms such as…
We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
In this paper, we study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems. Arjevani et al. (2019) established the lower bound $\Omega\left(\epsilon^{-2/(3p+1)}\right)$…
Wave functions based on electron-pair states provide inexpensive and reliable models to describe quantum many-body problems containing strongly-correlated electrons, given that broken-pair states have been appropriately accounted for by,…
Post-Newtonian (PN) theory provides the analytic foundation for modeling the early inspiral of binary black holes. However, as an asymptotic series, successive PN orders do not necessarily improve agreement with the full nonlinear dynamics.…
The efficient computer optimization of magnetic resonance pulses and pulse sequences involves the calculation of a problem-adapted cost function as well as its gradients with respect to all controls applied. The gradients generally can be…
We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in (Kaibel and Pfetsch, 2008). These polytopes are the convex hulls of all 0/1-matrices with…
Complex polynomial optimization has recently gained more and more attention in both theory and practice. In this paper, we study the optimization of a real-valued general conjugate complex form over various popular constraint sets including…
We introduce an orbital-optimized double-hybrid (DH) scheme using the optimized-effective-potential (OEP) method. The orbitals are optimized using a local potential corresponding to the complete exchange-correlation energy expression…
We propose a state-averaged orbital optimization scheme for improving the accuracy of excited states of the electronic structure Hamiltonian for use on near-term quantum computers. Instead of parameterizing the orbital rotation operator in…
Incomplete pairwise comparison matrices are increasingly employed to save resources and reduce cognitive load by collecting only a subset of all possible pairwise comparisons. We present their graph representation and some completion…
Piecewise Polynomials (PPs) are utilized in several engineering disciplines, like trajectory planning, to approximate position profiles given in the form of a set of points. While the approximation target along with domain-specific…
We present a new linear scaling method for the energy minimization step of semiempirical and first-principles Hartree-Fock and Kohn-Sham calculations. It is based on the self-consistent calculation of the optimum localized orbitals of any…
Imprecise measurements of a point set P = (p1, ..., pn) can be modelled by a family of regions F = (R1, ..., Rn), where each imprecise region Ri contains a unique point pi. A retrieval models an accurate measurement by replacing an…
This paper presents a one-dimensional analog of the Rectangular-Polar (RP) integration strategy and its convergence analysis for weakly singular convolution integrals. The key idea of this method is to break the whole integral into integral…
Optimization problems associated with the interaction of linked particles are at the heart of polymer science, protein folding and other important problems in the physical sciences. In this review we explain how to recast these problems as…
By the use of complete orthonormal sets of nonrelativistic scalar orbitals introduced by the author in previous papers the new complete orthonormal basis sets for two-and four-component spinor wave functions, and Slater spinor orbitals…
We present a practical implementation of the perturbation theory derived by Lynden-Bell (2015) for describing, to arbitrary precision, the orbit of a particle in an arbitrary spherically-symmetric potential. Our implementation corrects…
Optimisation problems are ubiquitous in particle and astrophysics, and involve locating the optimum of a complicated function of many parameters that may be computationally expensive to evaluate. We describe a number of global optimisation…