The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic...

We describe a branch-and-bound (b&b) method aimed at searching for an exact solution of the fundamental problem of decomposing a matrix into the sum of a sparse matrix and a low-rank matrix. Previous heuristic techniques employed convex and nonconvex optimization. We leverage and extend those...

McCormick (Math Prog 10(1):147–175, <CitationRef CitationID="CR23">1976</CitationRef>) provides the framework for convex/concave relaxations of factorable functions, via rules for the product of functions and compositions of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$F\circ f$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>F</mi> <mo>∘</mo> <mi>f</mi> </mrow> </math> </EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$F$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>F</mi> </math> </EquationSource> </InlineEquation> is a univariate function. Herein, the composition...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></citationref>

A large number of problems in ab-initio quantum chemistry involve finding the global minimum of the total system energy. These problems are traditionally solved by numerical approaches equivalent to local optimization. While these approaches are relatively efficient, they do not provide...