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In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
Regret matching (RM) -- and its modern variants -- is a foundational online algorithm that has been at the heart of many AI breakthrough results in solving benchmark zero-sum games, such as poker. Yet, surprisingly little is known so far in…
This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…
We show that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal (even to constant factors) convergence rates for the solution of convex optimization problems under nearly the same conditions required for…
We introduce a detailed analysis of the convergence of first-order methods with composite noise (sum of relative and absolute) in gradient for convex and smooth function minimization. This paper illustrates instances of practical problems…
This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices $\text{SO}(n)$. Such problems are nonconvex due to the constraint $X \in \text{SO}(n)$. Nonetheless, we show…
We revisit the error correction scheme of real-valued signals when the codeword is corrupted by gross errors on a fraction of entries and a small noise on all the entries. Combining the recent developments of approximate message passing and…
In this letter, we introduce the performance of maximal ratio combining (MRC) with weighting errors for physical layer security. We assume both legitimate user and eavesdropper each equipped with multiple antennas employ non ideal MRC. The…
A Gaussian multiple-input multiple-output wiretap channel in which the eavesdropper and legitimate receiver are equipped with arbitrary numbers of antennas and the transmitter has two antennas is studied in this paper. Under an average…
Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid…
In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…
This paper studies an optimization problem on the sum of traces of matrix quadratic forms in $m$ semi-orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the…
In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent…
In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove $\Delta$-convergence of the generated sequence to a critical point (which is defined in the text)…
In this paper, an energy harvesting scheme for a multi-user multiple-input-multiple-output (MIMO) secrecy channel with artificial noise (AN) transmission is investigated. Joint optimization of the transmit beamforming matrix, the AN…
The communication scenario under consideration in this paper corresponds to a multiuser channel with side information and consists of a broadcast channel with two legitimate receivers and an eavesdropper. Mainly, the results obtained are as…