Gradient sampling (GS) methods for the minimization of objective functions that may be nonconvex and/or nonsmooth are proposed, analyzed, and tested. One most computationally expensive components contemporary GS is need to solve a convex quadratic subproblem in each iteration. By contrast, proposed this paper allow use inexact solutions these subproblems, which, as proved paper, can incorporate...

The control of the A/B comonomer distribution over individual chains targeting block and/or gradient monomer distributions is essential to macroscopic properties resulting copolymers. Matrix-based kinetic Monte Carlo simulations allow compare each chain a representative copolymer sample with desired (mathematical) composition, as defined by inclusion probabilities (PA/B) taking B-functionalizat...

This work uses the dual-phase-lag (DPL) model of heat conduction to demonstrate the effect of temperature gradient relaxation time on the result of non-Fourier hyperbolic conduction in a finite slab subjected to a periodic thermal disturbance. DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. For the ...

In this paper the nano conical shell model is developed based on modified strain gradient theory. The governing equations of the nano truncated conical shell are derived using the FSDT, and the size parameters through modified strain gradient theory have been taken into account. Hamilton’s principle is used to obtain the governing equations, and the shell’s equations of motion are derived with ...