On the Goldstein-Levitin-Polyak gradient projection method

On the Goldstein - Levitin - Polyak Gradient Projection Method DIMITRI

This paper considers some aspects of a gradient projection method proposed by Goldstein [l], Levitin and Polyak [3], and more recently, in a less general context, by McCormick [lo]. We propose and analyze some convergent step-size rules to be used in conjunction with the method. These rules are similar in spirit to the efficient Armijo rule for the method of steepest descent and under mild assu...

Levitin-Polyak Well-Posedness for Equilibrium Problems with Functional Constraints

We generalize the notions of Levitin-Polyak well-posedness to an equilibrium problem with both abstract and functional constraints. We introduce several types of generalized Levitin-Polyak well-posedness. Some metric characterizations and sufficient conditions for these types of wellposedness are obtained. Some relations among these types of well-posedness are also established under some suitab...

Levitin-Polyak well-posedness of vector equilibrium problems

Further Study on the Levitin-Polyak Well-Posedness for Vector Equilibrium Problems

In this paper, we study Levitin-Polyak well-posedness for vector equilibrium problems with functional constraints. Two sufficient conditions of (generalized) Levitin-Polyak well-posedness are derived for vector equilibrium problems.

An eigenvalue study on the sufficient descent property of a‎ ‎modified Polak-Ribière-Polyak conjugate gradient method

‎Based on an eigenvalue analysis‎, ‎a new proof for the sufficient‎ ‎descent property of the modified Polak-Ribière-Polyak conjugate‎ ‎gradient method proposed by Yu et al‎. ‎is presented‎.