Given a convex optimization problem and its dual, there are many possible firstorder algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is done through convex duality and implies notably that for certain problems, such as for supervised machine learning problems with nonsmooth losses or problems ...

In this paper, we investigate the optimal probabilistic constellation shaping design for covert communication systems from a practical view. Different conventional communications with equiprobable constellations modulation, propose non-equiprobable modulation schemes to further enhance rate. Specifically, derive rate expressions discrete inputs first time. Then, study maximization problem by jo...

Frank-Wolfe algorithms for convex minimization have recently gained considerable attention from the Optimization and Machine Learning communities, as their properties make them a suitable choice in a variety of applications. However, as each iteration requires to optimize a linear model, a clever implementation is crucial to make such algorithms viable on large-scale datasets. For this purpose,...

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference [20, 4] has been proposed as a new paradigm to approximate the posterior by a mixture of densities by greedily adding components to the mixture. However, as is the case with many other variational inference algorithms, its theo...

Mixed-Integer optimization is a powerful tool for modeling many optimization problems arising from real-world applications. Finding a first feasible solution represents the first step for several MIP solvers. The Feasibility pump is a heuristic for finding feasible solutions to mixed integer linear problems which is effective even when dealing with hard MIP instances. In this work, we start by ...

We study –both in theory and practice– the use of momentum motions in classic iterative hard thresholding (IHT) methods. By simply modifying plain IHT, we investigate its convergence behavior on convex optimization criteria with non-convex constraints, under standard assumptions. In diverse scenaria, we observe that acceleration in IHT leads to significant improvements, compared to state of the...

In this paper, we introduce and investigate a new regularity condition in the asymptotic sense for optimization problems whose objective functions are polynomial. The normalization argument analysis enables us to study existence as well stability of solutions these problems. We prove Frank–Wolfe type theorem regular an Eaves non-regular pseudoconvex Moreover, under condition, show results on su...