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Perturbation Analysis Of Optimization Problems

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Metric Spaces Of Non Positive Curvature

Remarks on Some Fixed Point Theorems

Several iterative methods have been proposed in the literature for solving the variational inequalities in Hilbert or Banach spaces, where the underlying operator A is monotone and Lipschitz continuous. However, there are very few methods known for solving the variational inequalities, when the Lipschitz continuity of A is dispensed with. In this article, we introduce a projection-type algorithm for finding a common solution of the variational inequalities and fixed point problem in a reflexive Banach space, where A is pseudo-monotone and not necessarily Lipschitz continuous. Also, we present an application of our result to approximating solution of pseudo-monotone equilibrium problem in a reflexive Banach space. Finally, we present some numerical examples to illustrate the performance of our method as well as comparing it with related method in the literature.

https://link.springer.com/content/pdf/10.1007/s10957-020-01672-3.pdf

A Strong Convergence Theorem for Solving Pseudo-monotone Variational Inequalities Using Projection Methods

In this paper, we study a classical monotone and Lipschitz continuous variational inequality and fixed point problems defined on a level set of a convex function in the setting of Hilbert space. We...

Modified inertial subgradient extragradient method with self adaptive stepsize for solving monotone variational inequality and fixed point problems

In this paper, we introduce a viscosity-type proximal point algorithm comprising of a finite composition of resolvents of monotone bifunctions and a generalized asymptotically nonspreading mapping ...

A viscosity-type proximal point algorithm for monotone equilibrium problem and fixed point problem in an Hadamard space

In this paper, we propose and study an iterative algorithm that comprises of a finite family of inverse strongly monotone mappings and a finite family of Lipschitz demicontractive mappings in an Hadamard space. We establish that the proposed algorithm converges strongly to a common solution of a finite family of variational inequality problems, which is also a common fixed point of the demicontractive mappings. Furthermore, we provide a numerical experiment to demonstrate the applicability of our results. Our results generalize some recent results in literature.

https://www.mdpi.com/2075-1680/9/4/143/pdf

On a Viscosity Iterative Method for Solving Variational Inequality Problems in Hadamard Spaces

In this paper, we present two new inertial projection-type methods for solving multivalued variational inequality problems in finite-dimensional spaces. We establish the convergence of the sequence generated by these methods when the multivalued mapping associated with the problem is only required to be locally bounded without any monotonicity assumption. Furthermore, the inertial techniques that we employ in this paper are quite different from the ones used in most papers. Moreover, based on the weaker assumptions on the inertial factor in our methods, we derive several special cases of our methods. Finally, we present some experimental results to illustrate the profits that we gain by introducing the inertial extrapolation steps.

/pdf/new-inertial-projection-methods-for-solving-multivalued-3z1ybpei1q.pdf

New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

https://ijnaa.semnan.ac.ir/article_3080_cbdad3d80d8f73b4f043cf6b8daff31e.pdf

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

We propose two very simple methods, the first one with constant step sizes and the second one with self-adaptive step sizes, for finding a zero of the sum of two monotone operators in real reflexive Banach spaces. Our methods require only one evaluation of the single-valued operator at each iteration. Weak convergence results are obtained when the set-valued operator is maximal monotone and the single-valued operator is Lipschitz continuous, and strong convergence results are obtained when either one of these two operators is required, in addition, to be strongly monotone. We also obtain the rate of convergence of our proposed methods in real reflexive Banach spaces. Finally, we apply our results to solving generalized Nash equilibrium problems for gas markets. 

/pdf/convergence-of-two-simple-methods-for-solving-monotone-130wta1e.pdf

Chinedu Izuchukwu

Papers

A viscosity-type proximal point algorithm for monotone equilibrium problem and fixed point problem in an Hadamard space

On a Viscosity Iterative Method for Solving Variational Inequality Problems in Hadamard Spaces

New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

Convergence of Two Simple Methods for Solving Monotone Inclusion Problems in Reflexive Banach Spaces