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Optimization

Applied Mathematics

Iowa State University

Articles 1 - 3 of 3

Full-Text Articles in Engineering

Applications Of Fixed Point Theory To Distributed Optimization, Robust Convex Optimization, And Stability Of Stochastic Systems, Seyyed Shaho Alaviani Jan 2019

Applications Of Fixed Point Theory To Distributed Optimization, Robust Convex Optimization, And Stability Of Stochastic Systems, Seyyed Shaho Alaviani

Graduate Theses and Dissertations

Large-scale multi-agent networked systems are becoming more and more popular due to applications in robotics, machine learning, and signal processing. Although distributed algorithms have been proposed for efficient computations rather than centralized computations for large data optimization, existing algorithms are still suffering from some disadvantages such as distribution dependency or B-connectivity assumption of switching communication graphs. This study applies fixed point theory to analyze distributed optimization problems and to overcome existing difficulties such as distribution dependency or B-connectivity assumption of switching communication graphs. In this study, a new mathematical terminology and a new mathematical optimization problem are defined. It is ...


Convergence Analysis Of Alternating Direction Method Of Multipliers For A Family Of Nonconvex Problems, Mingyi Hong, Zhi-Quan Luo, Mesiam Razaviyayn Jan 2016

Convergence Analysis Of Alternating Direction Method Of Multipliers For A Family Of Nonconvex Problems, Mingyi Hong, Zhi-Quan Luo, Mesiam Razaviyayn

Industrial and Manufacturing Systems Engineering Publications

The alternating direction method of multipliers (ADMM) is widely used to solve large-scale linearly constrained optimization problems, convex or nonconvex, in many engineering fields. However there is a general lack of theoretical understanding of the algorithm when the objective function is nonconvex. In this paper we analyze the convergence of the ADMM for solving certain nonconvex consensus and sharing problems. We show that the classical ADMM converges to the set of stationary solutions, provided that the penalty parameter in the augmented Lagrangian is chosen to be sufficiently large. For the sharing problems, we show that the ADMM is convergent regardless ...


Automated Trajectory Design For Impulsive And Low Thrust Interplanetary Mission Analysis, Samuel Arthur Wagner Jan 2014

Automated Trajectory Design For Impulsive And Low Thrust Interplanetary Mission Analysis, Samuel Arthur Wagner

Graduate Theses and Dissertations

This dissertation describes a hybrid optimization algorithm that is able to determine optimal trajectories for many complex mission analysis and design orbital mechanics problems. This new algorithm will be used to determine optimal trajectories for a variety of mission design problems, including asteroid rendezvous, multiple gravity-assist (MGA), multiple gravity-assist with deep-space maneuvers (MGA-DSM), and low-thrust trajectory missions. The research described here was conducted at the Asteroid Deflection Research Center (ADRC) at Iowa State University.