Tractable Approximations to Robust Conic Optimization Problems

Tractable Approximations to Robust Conic Optimization Problems

In earlier proposals, the robust counterpart of conic optimization problems exhibits a lateral increase in complexity, i.e., robust linear programming problems (LPs) become second order cone problems (SOCPs), robust SOCPs become semidefinite programming problems (SDPs), and robust SDPs become NP-hard. We propose a relaxed robust counterpart for general conic optimization problems that (a) prese...

Distributionally Robust Optimization and Its Tractable Approximations

In this paper, we focus on a linear optimization problem with uncertainties, having expectationsin the objective and in the set of constraints. We present a modular framework to obtain an approx-imate solution to the problem that is distributionally robust, and more flexible than the standardtechnique of using linear rules. Our framework begins by firstly affinely-extending the ...

Further Simulation Results for “Outage Constrained Robust Transmit Optimization for Multiuser MISO Downlinks: Tractable Approximations by Conic Optimization” Technical Report

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...

Online appendix of “Distributionally Robust Optimization and its Tractable Approximations”

WEAK AND STRONG DUALITY THEOREMS FOR FUZZY CONIC OPTIMIZATION PROBLEMS

The objective of this paper is to deal with the fuzzy conic program- ming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. Un- der this setting, duality t...