This paper studies the one-sided sigma-smooth + concave function maximization problems under general convex sets. Provided that the objective function is Lipschitz smooth, we use the jump-start initial point selection...
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This paper studies the one-sided sigma-smooth + concave function maximization problems under general convex sets. Provided that the objective function is Lipschitz smooth, we use the jump-start initial point selection technique and the Frank-Wolfe method to propose a [1 - e-(1-alpha)eta-1], [1 - e-(1-alpha)eta-1. approximation algorithm with O(epsilon-1(n + T)) time complexity, where eta = ( alpha+1)2 sigma, alpha E (0,1), and sigma is a finite constant. The algorithm is discrete-time and receives O losses. To overcome the disadvantage that the gradient of function is Lipschitz continuous, we propose the continuous-time JumpStart Greedy Frank-Wolfe algorithm with the same approximation guarantee. In addition, through the analysis of our algorithms, we investigate some important theoretical properties regarding the analysis o. approximation algorithms for continuous function maximization problems.
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