Struggling with minimization problems? This paper addresses the problem of finding a point that satisfies sufficient decrease and curvature conditions in line search methods for minimization problems. It formulates the problem as finding a point in a specific set T(μ) and describes a search algorithm. The search algorithm produces a sequence of iterates that converge to a point in T(μ) and typically terminates in a finite number of steps. The paper presents an algorithm to solve for points. Numerical results on a set of test functions show that the algorithm terminates within a small number of iterations. This implementation of the search algorithm on a set of test functions shows that the algorithm terminates within a small number of iterations. This ensures that the user finds the solution within an acceptable time. The search algorithm is effective and efficient.
As a publication in ACM Transactions on Mathematical Software, this paper fits the journal's focus on algorithms, mathematical software, and numerical computation. This paper offers an effective solution and aligns with the focus of the journal.