Conic Optimization Theory: Convexification Techniques and Numerical Algorithms

Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic programming. The recent advances in various topics of modern optimization have also been revamping the area of machine learning. Motivated by the crucial role of optimization theory in the design, analysis, control and operation of real-world systems, this tutorial paper offers a detailed overview of some major advances in this area, namely conic optimization and its emerging applications. First, we discuss the importance of conic optimization in different areas. Then, we explain seminal results on the design of hierarchies of convex relaxations for a wide range of nonconvex problems. Finally, we study different numerical algorithms for large-scale conic optimization problems.Comment: 18 page

GSLAM: Initialization-robust Monocular Visual SLAM via Global Structure-from-Motion

Many monocular visual SLAM algorithms are derived from incremental structure-from-motion (SfM) methods. This work proposes a novel monocular SLAM method which integrates recent advances made in global SfM. In particular, we present two main contributions to visual SLAM. First, we solve the visual odometry problem by a novel rank-1 matrix factorization technique which is more robust to the errors in map initialization. Second, we adopt a recent global SfM method for the pose-graph optimization, which leads to a multi-stage linear formulation and enables L1 optimization for better robustness to false loops. The combination of these two approaches generates more robust reconstruction and is significantly faster (4X) than recent state-of-the-art SLAM systems. We also present a new dataset recorded with ground truth camera motion in a Vicon motion capture room, and compare our method to prior systems on it and established benchmark datasets.Comment: 3DV 2017 Project Page: https://frobelbest.github.io/gsla

Robust Stochastic Design of Linear Controlled Systems for Performance Optimization

This study discusses a robust controller synthesis methodology for linear, time invariant systems, under probabilistic parameter uncertainty. Optimization of probabilistic performance robustness for [script H]_2 and multi-objective [script H]_2 measures is investigated, as well as for performance measures based on first-passage system reliability. The control optimization approaches proposed here exploit recent advances in stochastic simulation techniques. The approach is illustrated for vibration response suppression of a civil structure. The results illustrate that, for problems with probabilistic uncertainty, the explicit optimization of probabilistic performance robustness can result in markedly different optimal feedback laws, as well as enhanced performance robustness, when compared to traditional “worst-case” notions of robust optimal control

Neo: A Learned Query Optimizer

Query optimization is one of the most challenging problems in database systems. Despite the progress made over the past decades, query optimizers remain extremely complex components that require a great deal of hand-tuning for specific workloads and datasets. Motivated by this shortcoming and inspired by recent advances in applying machine learning to data management challenges, we introduce Neo (Neural Optimizer), a novel learning-based query optimizer that relies on deep neural networks to generate query executions plans. Neo bootstraps its query optimization model from existing optimizers and continues to learn from incoming queries, building upon its successes and learning from its failures. Furthermore, Neo naturally adapts to underlying data patterns and is robust to estimation errors. Experimental results demonstrate that Neo, even when bootstrapped from a simple optimizer like PostgreSQL, can learn a model that offers similar performance to state-of-the-art commercial optimizers, and in some cases even surpass them