A Newton Frank–Wolfe method for constrained self-concordant minimization

We develop a new Newton Frank–Wolfe algorithm to solve class of constrained self-concordant minimization problems using linear oracles (LMO). Unlike L-smooth convex functions, where the Lipschitz continuity objective gradient holds globally, functions only has local bounds, making it difficult estimate number oracle (LMO) calls for underlying optimization algorithm. Fortunately, we can still prove that LMO our method is nearly same as standard Frank-Wolfe in case. Specifically, requires at most $${\mathcal {O}}\big (\varepsilon ^{-(1 + \nu )}\big )$$ LMO’s, $$\varepsilon $$ desired accuracy, and $$\nu \in (0, 0.139)$$ given constant depending on chosen initial point proposed Our intensive numerical experiments three applications: portfolio design with competitive ratio, D-optimal experimental design, logistic regression elastic-net regularizer, show outperforms different state-of-the-art competitors.