Gabidullina Z.R. Adaptive Conditional Gradient Method. Journal of Optimization Theory and Applications. December 2019, Volume 183, Issue 3, pp 1077–1098, ISSN: 0022-3239 (Print) (WOS)  DOI 10.1007/s10957-019-01585-w

https://link.springer.com/article/10.1007/s10957-019-01585-w

Abstract: We present a novel fully adaptive conditional gradient method with the step length regulation for solving pseudo-convex constrained optimization problems. We propose some deterministic rules of the step length regulation in a normalized direction. These rules guarantee to find the step length by utilizing the finite procedures and provide the strict relaxation of the objective function at each iteration. We prove that the sequence of the function values for the iterates generated by the algorithm converges globally to the objective function optimal value with sublinear rate.

Keywords:   Optimization problems, Pseudo-convex function, Adaptation, Descent direction, Normalization, Step length Regulation, Rate of convergence.