The Markowitz Mean Variance model (MMV) and its variants are widely used for portfolio selection. The mean and covariance matrix used in the model originate from probability distributions that need to be determined empirically. It is well known that these parameters are notoriously difficult to estimate. In addition, the model is very sensitive to these parameter estimates. As a result, the per...

The electric power grid is recognized as an essential modern infrastructure that poses numerous canonical design and operational problems. Perhaps most critically, the inherently large scale of the power grid and similar systems necessitates fast algorithms. A particular complication distinguishing problems in power systems from those arising in other large infrastructures is the mathematical d...

To obtain a primal-dual pair of conic programming problems having zero duality gap, two methods have been proposed: the facial reduction algorithm due to Borwein and Wolkowicz [1, 2] and the conic expansion method due to Luo, Sturm, and Zhang [5]. We establish a clear relationship between them. Our results show that although the two methods can be regarded as dual to each other, the facial redu...

Given a primal-dual pair of linear programs, it is well known that if their optimal values are viewed as lying on the extended real line, then the duality gap is zero, unless both problems are infeasible, in which case the optimal values are +∞ and −∞. In contrast, for optimization problems over nonpolyhedral convex cones, a nonzero duality gap can exist when either the primal or the dual is fe...

Spectral functions on Euclidean Jordan algebras arise frequently in convex optimization models. Despite the success of primal-dual conic interior point solvers, there has been little work enabling direct support for spectral cones, that is, proper nonsymmetric cones defined from epigraphs and perspectives functions. We propose simple logarithmically homogeneous barriers we derive efficient, num...

We present a primal-dual interior-point algorithm for second-order conic optimization problems based on a specific class of kernel functions. This class has been investigated earlier for the case of linear optimization problems. In this paper we derive the complexity bounds O( √ N (logN) log N ) for largeand O( √ N log N ) for smallupdate methods, respectively. Here N denotes the number of seco...

This technical report serves to provide further simulation results for the paper “Outage constrained robust transmit optimization for multiuser MISO downlinks: Tractable approximations by conic optimization”. In addition to the rate constrained formulation, which is the main focus of the aforementioned main manuscript, we also demonstrate how the proposed methods can be used to tackle the max-m...

This paper contributes to classification and identification in modern finance through advanced optimization. In the last few decades, financial misalignments and, thereby, financial crises have been increasing in numbers due to the rearrangement of the financial world. In this study, as one of the most remarkable of these, countries’ debt crises, which result from illiquidity, are tried to pred...