Gap functions for quasi-equilibria

作者：Bigi Giancarlo; Passacantando Mauro^*

来源：Journal of Global Optimization, 2016, 66(4): 791-810.

DOI：10.1007/s10898-016-0458-9

• Quasi-equilibrium
• Gap function
• Stationary point
• Descent algorithm
• Error bound

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.

• 出版日期2016-12