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Index Terms—Energy efficiency, exact line search, LASSO, massive MIMO, MIMO broadcast channel, nonconvex optimiza- tion, nondifferentiable optimization, pseudo-convex

Supermodular functions, and their duals, submodular functions, play a central rˆ ole in many fields of discrete mathematics, most notably combinatorial optimization (rank function

However, if on the one hand convex optimization usually refers to minimizing a convex func- tion on a convex set K without precising its representation (g j ) (see e.g. [3, Chapter

A combinatorial algorithm minimizing submodular functions in strongly polynomial time. Journal of Combinatorial Theory, Series B,

Theorem ( Gr¨otschel-Lov´asz-Schrijver, Fujishige-Fleicher-Iwata, Schrijver ) The minimum value of a submodular function can be found

We have so far studied the minimization of separable convex functions over submodular polytopes, motivated by bottlenecks in projection-based first-order optimization methods in

(1) In Section 3, we cast the problem of minimizing decomposable submodular functions as an or- thogonal projection problem and show how existing optimization techniques may be

In this paper, we show that for maximizing non-monotone DR-submodular functions over a general convex set (such as up-closed convex sets, conic convex set, etc) the Frank-Wolfe