In this report, we propose a new partitioned variable metric method for minimizing nonsmooth partially separable functions. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Computational experiments given confirm efficiency and robustness of the new met...

A new rank-two variable-metric method is derived using Greenstadt's variational approach [Math. Comp., this issue]. Like the Davidon-Fletcher-Powell (DFP) variable-metric method, the new method preserves the positive-definiteness of the approximating matrix. Together with Greenstadt's method, the new method gives rise to a one-parameter family of variable-metric methods that includes the DFP an...

As a fundamental concept, geometry is widely used in understanding physical phenomena. In quantum mechanics, related to the system’s state and can be characterized by geometric tensor (QGT), whose real part referred as metric (QMT), which defines distance between two neighboring states projected Hilbert space. Several pieces of research based on discrete variables have been proposed extract QMT...

We propose a diagonal metric selection for variable metric proximal gradient method (VMPG). The proposed metric better captures the local geometry of the problem and provides improved convergence compared to the standard proximal gradient (PG) methods with Barzilai-Borwein (BB) stepsize selection. Further, we provide convergence guarantees for the proposed method and illustrate its advantages o...

In the design of heat exchangers, it is necessary to determine the heat transfer rate between hot and cold fluids in order to calculate the overall heat transfer coefficient and the heat exchanger efficiency. Heat transfer rate can be determined by inverse methods. In this study, the unknown space-time dependent heat flux imposed on the wall of a heat exchanger internal tube is estimated by app...

It is indispensable for users to evaluate the trustworthiness of other users (referred to as advisors), to cope with possible misleading opinions provided by them. Advisors’ misleading opinions may be induced by their dishonesty, subjectivity difference with users, or both. Existing approaches do not well distinguish the two different causes. In this paper, we propose a novel probabilistic grap...