arXiv subjects

Oday Hazaimah

Publications and source records attributed to Oday Hazaimah.

7 recordsLinked to original sources

arXiv2025

Translation Mappings of Quasimonotonicity Beyond Smoothness

Monotonicity of a mapping implies its pseudomonotonicity and hence quasimonotonocity, the converse is not true. In this note we intend to study the situations under which quasimono tonicity of a mapping implies its monotonicity. Thus we generalize some results in the literature related to the connection between monotonocity and its generalized classes for multi-valued mappings via translation maps in real topological spaces. No differentiability assumption is required but continuity assumption is imposed.

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arXiv2025

Iterative Schemes for Uniformly Nonconvex Equilibrium Problems

Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular equilibrium problems are analyzed by the aux iliary principle and inertial proximal methods. The convergence analysis of the new proposed methods is considered under some mild conditions. Gap functions are constructed to suggest some descent-type scheme for uniformly regular equilibrium problems. Our results can be viewed as significant refinements and improvements of the previously known results and they continue to hold for equilibrium problems, variational inequalities and complementarity problems as well.

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arXiv2025

Continuous and Discrete Systems for Quasi Variational Inequalities with Application to Game Theory

A new class of projected dynamical systems of third order is investigated for quasi (parametric) variational inequalities in which the convex set in the classical variational inequality also depends upon the solution explicitly or implicitly. We study the stability of a continuous method of a gradient type. Some iterative implicit and explicit schemes are suggested as counterparts of the continuous case by inertial proximal methods. The convergence analysis of these proposed methods is established under sufficient mild conditions. Moreover, some applications dealing with the generalized Nash equilibrium problems are presented.

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arXiv2025

Nonmonotone Spectral Analysis for Variational Inclusions

Gradient descent algorithms perform well in convex optimization but can get tied for finding local minima in non-convex optimization. A robust method that combines a spectral approach with nonmonotone line search strategy for solving variational inclusion problems is proposed. Spectral properties using eigenvalues information are used for accelerating the convergence. Nonmonotonic behaviour is exhibited to relax descent property and escape local minima. Nonmonotone spectral conditions leverage adaptive search directions and global convergence for the proposed spectral subgradient algorithm.

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arXiv2024

A Third Order Dynamical System for Mixed Variational Inequalities

In this paper, we introduce and study a class of resolvent dynamical systems to investigate some inertial proximal methods for solving mixed variational inequalities. These proposed methods along with their discretizations and derived rates of convergences require only the monotonicity for mixed variational inequalities under some mild conditions. We establish the global asymptotically and exponentially stability of the solution of the resolvent dynamical system for monotone operators. Ideas and techniques of this paper may be extended for other classes of variational inequalities and equilibrium problems.

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arXiv2024

Polytropic Dynamical Systems with Time Singularity

In this paper we consider a class of second order singular homogeneous differential equations called the Lane-Emden-type with time singularity in the drift coefficient. Lane-Emden equations are singular initial value problems that model phenomena in astrophysics such as stellar structure and are governed by polytropics with applications in isothermal gas spheres. A hybrid method is proposed to approximate the solution of this type of dynamic equations.

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arXiv2021

On the Weak and Strong Convergence of a Conceptual Algorithm for Solving Three Operator Monotone Inclusions

In this paper, a conceptual algorithm modifying the forward-backward-half-forward (FBHF) splitting method for solving three operator monotone inclusion problems is investigated. The FBHF splitting method adjusts and improves Tseng's forward-backward-forward (FBF) splitting method when the inclusion problem has a third-part operator that is cocoercive. The FBHF method recovers the FBF iteration (when this aforementioned part is zero), and it also works without using the widely used Lipschitz continuity assumption. The conceptual algorithm proposed in this paper also has those advantages, and it derives two variants (called Method 1 and Method 2) by choosing different projection (forward) steps. Both proposed methods also work efficiently without assuming the Lipschitz continuity and without directly using the cocoercive constant. Moreover, they have the following desired features: (i) very general iterations are derived for both methods, recovering the FBF and the FBHF iterations and allowing possibly larger stepsizes if the projection steps are over-relaxing; and (ii) strong convergence to the best approximation solution of the problem is proved for Method 2. To the best of our knowledge, this is the first time that an FBF-type method converges strongly for finding the best approximation solution of the three operator monotone inclusion.

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