A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space

summary:In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of $\delta$-demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition $\sum _{n=1}^\infty \beta _n\Vert x_{n-1} -x_n\Vert < + \infty$ on the inertial term. Finally, we provide some applications and numerical example to show the efficiency and accuracy of our algorithm. Our results improve and complement many other related results in the literature

Viscosity extragradient with modified inertial method for solving equilibrium problems and fixed point problem in Hadamard manifold

In this article, we propose a viscosity extragradient algorithm together with an inertial extrapolation method for approximating the solution of pseudomonotone equilibrium and fixed point problem of a nonexpansive mapping in the setting of a Hadamard manifold. We prove that the sequence generated by our iterative method converges to a solution of the above problems under some mild conditions. Finally, we outline some implications of our results and present several numerical examples showing the implementability of our algorithm. The results of this article extend and complement many related results in linear spaces.</p

Modified inertial Tseng method for solving variational inclusion and fixed point problems on Hadamard manifolds

In this article, we introduce a forward–backward splitting method with a new step size rule for finding a singularity point of an inclusion problem which is defined by means of a sum of a single-valued vector field and a multi-valued vector field on a Hadamard manifold. Using a Mann, viscosity and an inertial extrapolation method, we establish a convergence result without prior knowledge of the Lipschitz constant of the underlying operator. We present some applications of our result to variational inequality problem. Finally, we present some numerical examples to demonstrate the numerical behavior of our proposed method. The result discuss in this article extends and complements many related results in the literature.</p

Characterization of starches from some selected white and yellow cassava roots for dry starch noodle production

Starch noodle, originally produced from mung bean starch, is now patronized in many parts of the world. Although cassava is one of the most abundant sources of starch in Nigeria, previous works determining its applicability for noodle production are scarce in literature. This study therefore determined the chemical properties of starches from selected white and yellow cassava for dry starch noodle production. Descriptive attributes and sensory acceptability of the starch noodle produced were also determined using commercial starch noodle as reference sample. Data obtained were subjected to analysis of variance using SPSS (version 21). Chemical properties of cassava starches varied significantly (p < .05). Using clustering and discriminant function analyses, two product clusters were identified with their distinct physical and sensory properties. This study showed that the most acceptable cassava starch noodles were obtained from TMS 01/1206 followed by TMS 01/1368, the least acceptable noodle was obtained from TME 419