A maximum a-posteriori approach for overcomplete blind source separation based on Laplacian priors usually involves 1-normminimization. It requires different approaches for real and complex numbers as they appear for example in the frequency domain. In this paper we compare a combinatorial approach for real numbers with a second order cone programming approach for complex numbers. Although the ...

In this paper, a joint optimal design is investigated for orthogonal frequency division multiplexing (OFDM) systems to reduce peak interference-to-carrier ratio (PICR), out-of-band power (OBP) emissions, and peak-to-average power ratio (PAPR). Two approaches, namely, the phase rotation approach and the constellation extension approach, are proposed to convert this joint design problem into a se...

It is challenging to generate optimal trajectories for nonlinear dynamic systems under external disturbances. In this brief, we present a novel approach planning safe of the chance-constrained trajectory optimization problems with nonconvex constraints. First, chance constraints are handled by deterministic ones which show its availability. We derive an iterative convex method solve control pro...

Space tensors appear in physics and mechanics, and they are real physical entities. Mathematically, they are tensors in the three-dimensional Euclidean space. In the research of diffusion magnetic resonance imaging, convex optimization problems are formed where higher order positive semi-definite space tensors are involved. In this short paper, we investigate these problems from the viewpoint o...

We discuss two families of valid inequalities for linear mixed integer programming problems with cone constraints of arbitrary order, which arise in the context of stochastic optimization with downside risk measures. In particular, we extend the results of Atamtürk and Narayanan (Math. Program., 2010, 2011), who developed mixed integer rounding cuts and lifted cuts for mixed integer programming...

Three primal-dual interior-point algorithms for homogeneous cone programming are presented. They are a short-step algorithm, a large-update algorithm, and a predictor-corrector algorithm. These algorithms are described and analyzed based on a characterization of homogeneous cone via T -algebra. The analysis show that the algorithms have polynomial iteration complexity.

In this paper, under a suitable regularity condition, we establish that a broad class of conic convex polynomial optimization problems, called conic sum-of-squares convex polynomial programs, exhibits exact conic programming relaxation, which can be solved by various numerical methods such as interior point methods. By considering a general convex cone-program, we give unified results that appl...