Gap functions for quasi-equilibria

Giancarlo Bigi () and Mauro Passacantando ()
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Giancarlo Bigi: Università di Pisa
Mauro Passacantando: Università di Pisa

Journal of Global Optimization, 2016, vol. 66, issue 4, No 8, 810 pages

Abstract: Abstract An approach for solving quasi-equilibrium problems (QEPs) is proposed relying on gap functions, which allow reformulating QEPs as global optimization problems. The (generalized) smoothness properties of a gap function are analysed and an upper estimate of its Clarke directional derivative is given. Monotonicity assumptions on both the equilibrium and constraining bifunctions are a key tool to guarantee that all the stationary points of a gap function actually solve QEP. A few classes of constraints satisfying such assumptions are identified covering a wide range of situations. Relying on these results, a descent method for solving QEP is devised and its convergence proved. Finally, error bounds are given in order to guarantee the boundedness of the sequence generated by the algorithm.

Keywords: Quasi-equilibrium; Gap function; Stationary point; Descent algorithm; Error bound (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10898-016-0458-9

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