On convergence and complexity analysis of an accelerated forward–backward algorithm with linesearch technique for convex minimization problems and applications to data prediction and classification

Abstract

In this work, we introduce a new accelerated algorithm using a linesearch technique for solving convex minimization problems in the form of a summation of two lower semicontinuous convex functions. A weak convergence of the proposed algorithm is given without assuming the Lipschitz continuity on the gradient of the objective function. Moreover, the convexity of this algorithm is also analyzed. Some numerical experiments in machine learning are also discussed, namely regression and classification problems. Furthermore, in our experiments, we evaluate the convergent behavior of this new algorithm, then compare it with various algorithms mentioned in the literature. It is found that our algorithm performs better than the others.

Breast Cancer Screening Using a Modified Inertial Projective Algorithms for Split Feasibility Problems

“…where N is a number of iterations that we want to stop and σ n = σ n for algorithm (6). Sigmoid is set as an activation function with hidden nodes M = 160, and four evaluation metrics of each algorithm are shown in Table 4.…”

“…The weak convergence of algorithm fω n g generated by (6) was proved under the conditions of the extrapolation factor (8) and the stepsize parameter λ.…”

“…Many optimization algorithms were used to solve medical classification in machine learning; see [ 5 , 6 ]. In this paper, we focus on the split feasibility problem (SFP) applying to mammography classification.…”

An Accelerated Convex Optimization Algorithm with Line Search and Applications in Machine Learning

“…For instance, we could utilize an inertial step, which was first introduced by Polyak [13], to solve smooth convex minimization problems. Since then, there have been several works that included an inertial step in their algorithms to accelerate the convergence behavior; see [14][15][16][17][18][19] for examples.…”