We propose an inertial proximal point method for variational inclusion involving difference of two maximal monotone vector fields in Hadamard manifolds. We prove that if the sequence generated by the method is bounded, then every cluster point is a solution of the non-monotone variational inclusion....
inertial proximal point methodKurdyka-Lojasiewicz propertynonconvex optimizationnonsmoothThe alternating direction method of multipliers (ADMM) is an efficient method for solving separable problems. However, ADMM may not converge when there is a nonconvex function in the objective. The main contributions ...
The proximal point method (PPM) for solving maximal monotone operator inclusion problem is a highly powerful tool for algorithm design, analysis and interpretation. To accelerate convergence of the PPM, inertial PPM (iPPM) was proposed in the literature. In this note, we show that some of the ...
If V=0, this reduces to a relaxed inertial proximal point method analyzed by Attouch and Cabot [2]. If \rho _{k}=1, an inertial forward-backward splitting method is recovered, first studied by Lorenz and Pock [45]. Convergence guarantees for the forward-backward splitting rely on the co...
An extragradient-like approximation method for variational inequality problems and fixed point problems Appl. Math. Comput. (2007) B.-S. He et al. An approximate proximal-extragradient type method for monotone variational inequalities J. Math. Anal. Appl. (2004) J. Mashreghi et al. Forcing st...
By contrast, the proximal links and the platform are respectively associated with actuated joint and Cartesian velocities. To remove passive velocities, the point mass method is applied, where the distal links are replaced by point masses. The point masses should attach to the endpoints of distal ...
Additionally, the single sensor location on the ankle might also limit the ability of the method, since motion of more proximal segments cannot be accounted for. Placing the sensor on the pelvis, near to the centre of mass, for example, might be required (Lim et al. 2019; Alcantara et ...
R. (2009). Fixed point theory for Lipschitzian-type mappings with applications (Vol. 6, pp. x+-368). New York: Springer Alvarez, F., Attouch, H.: An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set-Valued Anal. 9(1–...
For instance, He [13] proposed the following proximal point method for solving the SEP (1.1)–(1.2): (1.8) where C and Q are two nonempty convex and closed subsets of the real Hilbert spaces and , respectively, and are two monotone bifunctions, , such that , and is the adjoint the...
10. A method of reducing a thermal gradient of an assembly, the method comprising: determining temperatures of a plurality of regions of the assembly; and adjusting the temperature of a plurality of heating elements proximal to the assembly based on the temperatures of the plurality of regions, ...