Long-step path-following algorithm for solving symmetric programming problems with nonlinear objective functions

Leonid Faybusovich () and Cunlu Zhou ()
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Leonid Faybusovich: University of Notre Dame
Cunlu Zhou: University of Notre Dame

Computational Optimization and Applications, 2019, vol. 72, issue 3, No 9, 769-795

Abstract: Abstract We developed a long-step path-following algorithm for a class of symmetric programming problems with nonlinear convex objective functions. The theoretical framework is developed for functions compatible in the sense of Nesterov and Nemirovski with $$-\,\ln \det $$ - ln det barrier function. Complexity estimates similar to the case of a linear-quadratic objective function are established, which gives an upper bound for the total number of Newton steps. The theoretical scheme is implemented for a class of spectral objective functions which includes the case of quantum (von Neumann) entropy objective function, important from the point of view of applications. We explicitly compare our numerical results with the only known competitor.

Keywords: Convex optimization; Symmetric programming; Nonlinear objective functions; Self-concordance; Interior-point methods; Matrix monotonicity; Von Neumann entropy (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-018-0054-7

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