Wilfer O. Multi-Composed Programming with Applications to Facility Location

Springer, 2020. — 202 p. — (Mathematical Optimization and Economathematics). — ISBN: 978-3-658-30579-6.Oleg Wilfer presents a new conjugate duality concept for geometric and cone constrained optimization problems whose objective functions are a composition of finitely many functions. As an application, the author derives results for single minmax location problems formulated by means of extended perturbed minimal time functions as well as for multi-facility minmax location problems defined by gauges. In addition, he provides formulae of projections onto the epigraphs of gauges to solve these kinds of location problems numerically by using parallel splitting algorithms. Numerical comparisons of recent methods show the excellent performance of the proposed solving technique.Notations and preliminary results
Lagrange duality for multi-composed optimization problems
Duality results for minmax location problems
Solving minmax location problems via epigraphical projection
Numerical experiments