In this paper, we present some gradient projection algorithms for solving optimization problems with a convex-constrained set. We derive the optimality condition when the convex set is a cone and under some mild assumptions, we prove the convergence of these algorithms. Finally, we apply them to quadratic problems arising in training support vector machines for the Wisconsin Diagnostic Breast Cancer (WDBC) classification problem.

In this paper, an efficient GV1-CG is developed to optimizing the modified conjugate gradient algorithm by using a new conjugate property. This is to to increase the speed of the convergence and retain the characteristic mass convergence using the conjugate property. This used property is proposed to public functions as it is not necessary to be a quadratic and convex function. The descent sharp property and comprehensive convergence for the proposed improved algorithm have been proved. Numerical results on some test function indicate that the new CG-method outperforms many of the similar methods in this field.

dosimetry through an electronic portal-imaging device (EPID) to achieve two-dimensional (2D) dose distribution for homogenous environments. Material and Methods: In this Phantom study, first, the EPID calibration curve and correction coefficients for field size were obtained from EPID and ionization chamber. Second, the EPID off-axis pixel response was measured, and the greyscale image of the EPID was converted into portal dose image using the calibration curve. Next, the scattering contribution was calculated to obtain the primary dose. Then, by means of a verified back-projection algorithm and the Scatter-to-Primary dose ratio, a 2D dose distribution at the mid-plane was obtained. Results: The results obtained from comparing the transmitted EPID dosimetry to the calculated dose, using commercial treatment planning system with gamma function while there is 3% dose difference and 3mm distance to agreement criteria, were in a good agreement. In addition, the pass rates of γ < 1 was 94. 89% for the homogeneous volumes. Conclusion: Based on the results, the method proposed can be used in EPID dosimetry.

Improving the convergence speed of adaptive filters is crucial for enhancing performance inapplications involving highly correlated input signals. In this paper, we propose a novel method to improvethe convergence performance of the affine projection LMS (AP-LMS) algorithm by incorporating a variablesmoothing approach for the weight update matrix. The smoothing parameter is dynamically assignedbased on the difference between the instantaneous and smoothed values of the weight update matrix.Simulation results for FIR system modeling demonstrate that the proposed algorithm achieves superiorconvergence performance in estimating system coefficients compared to competing adaptive algorithms for both stationary and non-stationary input signals.