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Finite convergence into a convex polytope via facet reflections

Dinesh B. Ekanayake, Douglas J. LaFountain, Boris Petracovici (2023)

Applications of Mathematics

The problem of utilizing facet reflections to bring a point outside of a convex polytope to inside has not been studied explicitly in the literature. Here we introduce two algorithms that complete the task in finite iterations. The first algorithm generates multiple solutions on the plane, and can be readily utilized in creating games on a plane or as a level generation method for video games. The second algorithm is a new efficient way to bring infeasible starting points of an optimization problem...

First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules

David A. Mazziotti (2007)

ESAIM: Mathematical Modelling and Numerical Analysis


The ground-state energy and properties of any many-electron atom or molecule may be rigorously computed by variationally computing the two-electron reduced density matrix rather than the many-electron wavefunction. While early attempts fifty years ago to compute the ground-state 2-RDM directly were stymied because the 2-RDM must be constrained to represent an N-electron wavefunction, recent advances in theory and optimization have made direct computation of the 2-RDM possible. The constraints in...

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