Stochastic Dual Dynamic Programming for Optimal Power Flow Problems under Uncertainty

We propose the first computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in alternating current (AC) power systems. To this end, we use recent results on dual convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the stochastic dual dynamic programming (SDDP) algorithm for problems with a Markovian … Read more

Solving sparse polynomial optimization problems with chordal structure using the sparse, bounded-degree sum-of-squares hierarchy

The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality … Read more

Construction of Covariance Matrices with a specified Discrepancy Function Minimizer, with Application to Factor Analysis

The main goal of this paper is to develop a numerical procedure for construction of covariance matrices such that for a given covariance structural model and a discrepancy function the corresponding minimizer of the discrepancy function has a specified value. Often construction of such matrices is a first step in Monte Carlo studies of statistical … Read more

A Near Maximum Likelihood Decoding Algorithm for MIMO Systems Based on Semi-Definite Programming

In Multi-Input Multi-Output (MIMO) systems, Maximum-Likelihood (ML) decoding is equivalent to finding the closest lattice point in an N-dimensional complex space. In general, this problem is known to be NP hard. In this paper, we propose a quasi-maximum likelihood algorithm based on Semi-Definite Programming (SDP). We introduce several SDP relaxation models for MIMO systems, with … Read more

A primal-dual second order cone approximations algorithm for symmetric cone programming

This paper presents the new concept of second-order cone approximations for convex conic programming. Given any open convex cone $K$, a logarithmically homogeneous self-concordant barrier for $K$ and any positive real number $r \le 1$, we associate, with each direction $x \in K$, a second-order cone $\hat K_r(x)$ containing $K$. We show that $K$ is … Read more