Matrix analyses on the Dai–Liao conjugate gradient method

Some optimal choices for a parameter of the Dai–Liao conjugate gradient method are proposed by conducting matrix analyses of the method. More precisely, first the $\ell_1$ and $\ell_\infty$ norm condition numbers of the search direction matrix are minimized, yielding two adaptive choices for the Dai–Liao parameter. Then we show that a recent formula for computing this parameter which guarantees the descent property can be considered as a minimizer of the spectral condition number as well as the well-known measure function for a symmetrized version of the search direction matrix. Brief convergence analyses are also carried out. Finally, some numerical experiments on a set of test problems related to constrained and unconstrained testing environment, are conducted using a well-known performance profile. doi:10.1017/S144618111900006

A restart scheme for the Dai–Liao conjugate gradient method by ignoring a direction of maximum magnification by the search direction matrix

As known, finding an effective restart procedure for the conjugate gradient methods has been considered as an open problem. Here, we aim to study the problem for the Dai–Liao conjugate gradient method. In this context, based on a singular value analysis conducted on the Dai–Liao search direction matrix, it is shown that when the gradient approximately lies in the direction of the maximum magnification by the matrix, the method may get into some computational errors as well as it may converge hardly. In such situation, ignoring the Dai–Liao search direction in the sense of performing a restart may enhance the numerical stability as well as may accelerate the convergence. Numerical results are reported; they demonstrate effectiveness of the suggested restart procedure in the sense of the Dolan–Moré performance profile

A nonmonotone ADMM-based diagonal quasi-Newton update with application to the compressive sensing problem

Considering a minimization problem according to the Byrd-Nocedal measure function together with the secant equation, a diagonal quasi-Newton updating formula is suggested. To find the optimal elements of the updating matrix, the well-known algorithm of the alternating direction method of multipliers (ADMM) is employed. Moreover, convergence analysis is conducted based on a modified nonmonotone Armijo line search incorporating the simulated annealing strategy. Lastly, performance of the method is numerically tested on a set of CUTEr functions and on a smooth transcendental approximation of the compressive sensing problem. Across the computational spectrum, the given method turns out to be successful

Investigating the relationship between watching satellite channels and intimacy and marital satisfaction of couples in Isfahan, Iran, in 2014

Background: In the age of communication and media that families are rapidly driven towards using satellite channels and other media, considering family health in this regard is essential. A determinant of health is marital satisfaction. The aim of this study was to investigate the relationship between watching satellite channels and intimacy and marital satisfaction in Isfahan, Iran. Materials and Methods: This cross-sectional and correlational study was conducted on one group of 480 couples (n = 960) participating from 8 health-treatment centers in Isfahan. Multi-stage cluster sampling was used in this study. Inclusion criteria included at least 2 years of marriage. After completion of Bagarozzi's Marital Intimacy Questionnaire and ENRICH Marital Inventory, the couples were divided into two groups based on watching satellite networks. Data were analyzed using SPSS 18. Results: There was a significant relationship between intimacy and marital satisfaction in both viewers and non-viewers of satellite channels (P < 0.050). Average duration of couple's interaction in the satellite viewing group was 22.4 minutes and in non-viewers group was 47.95 min. In addition, the duration of interaction had a significant relationship with marital satisfaction and intimacy (P < 0.050). Conclusions: This study showed that watching satellite channels reduced the intimacy and marital satisfaction of the couples, and duration of interaction among the couples