Regional division and reduction algorithm for minimizing the sum of linear fractional functions.

This paper presents a practicable regional division and cut algorithm for minimizing the sum of linear fractional functions over a polyhedron. In the algorithm, by using an equivalent problem (P) of the original problem, the proposed division operation generalizes the usual standard bisection, and the deleting and reduction operations can cut away a large part of the current investigated region in which the global optimal solution of (P) does not exist. The main computation involves solving a sequence of univariate equations with strict monotonicity. The proposed algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of univariate equations. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm.

Solving a class of generalized fractional programming problems using the feasibility of linear programs.

This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an exploration of a suitably defined nonuniform grid. The main work of the algorithm involves checking the feasibility of linear programs associated with the interesting grid points. It is proved that the proposed algorithm is a fully polynomial time approximation scheme as the ratio terms are fixed in the objective function to problem (P), based on the computational complexity result. In contrast to existing results in literature, the algorithm does not require the assumptions on quasi-concavity or low-rank of the objective function to problem (P). Numerical results are given to illustrate the feasibility and effectiveness of the proposed algorithm.

Linear decomposition approach for a class of nonconvex programming problems.

This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming subproblems. Based on solving a series of liner programming subproblems corresponding to those grid points we can obtain the near-optimal solution of the original problem. Compared to existing results in the literature, the proposed algorithm does not require the assumptions of quasi-concavity and differentiability of the objective function, and it differs significantly giving an interesting approach to solving the problem with a reduced running time.

Inhibition of advanced glycation end product formation by Pu-erh tea ameliorates progression of experimental diabetic nephropathy.

Accumulation of advanced glycation end products (AGEs) has been implicated in the development of diabetic nephropathy. We investigated the effects of Pu-erh tea on AGE accumulation associated with diabetic nephropathy. Although it did not affect blood glucose levels and insulin sensitivy, Pu-erh tea treatment for 8 weeks attenuated the increases in urinary albumin, serum creatinine, and mesangial matrix in db/db mice. We found that Pu-erh tea prevented diabetes-induced accumulation of AGEs and led to a decreased level of receptor for AGE expression in glomeruli. Both production and clearance of carbonyl compounds, the main precursor of AGE formation, were probably attenuated by Pu-erh tea in vivo independent of glyoxalase I expression. In vitro, HPLC assay demonstrated Pu-erh tea could trap methylglyoxal in a dose-dependent manner. Our study raises the possibility that inhibition of AGE formation by carbonyl trapping is a promising approach to prevent or arrest the progression of diabetic complications.