Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.
['Giancarlo Bigi', 'Mauro Passacantando']
I am writing a research paper on a idea Gap functions for quasi-equilibria
[{"from": "human", "value": "I am writing a research paper on a idea Gap functions for quasi-equilibria"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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."}]