7 research outputs found
Dual Descent ALM and ADMM
Classical primal-dual algorithms attempt to solve by alternatively minimizing over the primal variable
through primal descent and maximizing the dual variable through dual
ascent. However, when is highly nonconvex with complex
constraints in , the minimization over may not achieve global
optimality, and hence the dual ascent step loses its valid intuition. This
observation motivates us to propose a new class of primal-dual algorithms for
nonconvex constrained optimization with the key feature to reverse dual ascent
to a conceptually new dual descent, in a sense, elevating the dual variable to
the same status as the primal variable. Surprisingly, this new dual scheme
achieves some best iteration complexities for solving nonconvex optimization
problems. In particular, when the dual descent step is scaled by a fractional
constant, we name it scaled dual descent (SDD), otherwise, unscaled dual
descent (UDD). For nonconvex multiblock optimization with nonlinear equality
constraints, we propose SDD-ADMM and show that it finds an
-stationary solution in iterations. The
complexity is further improved to and
under proper conditions. We also propose UDD-ALM,
combining UDD with ALM, for weakly convex minimization over affine constraints.
We show that UDD-ALM finds an -stationary solution in
iterations. These complexity bounds for both
algorithms either achieve or improve the best-known results in the ADMM and ALM
literature. Moreover, SDD-ADMM addresses a long-standing limitation of existing
ADMM frameworks
Distributed Multi-agent Optimization and Control with Applications in Smart Grid
With recent advancements in network technologies like 5G and Internet of Things (IoT), the size and complexity of networked interconnected agents have increased rapidly. Although centralized schemes have simpler algorithm design, in practicality, it creates high computational complexity and requires high bandwidth for centralized data pooling. In this dissertation, for distributed optimization of networked multi-agent architecture, the Alternating Direction Method of Multipliers (ADMM) is investigated. In particular, a new adaptive-gain ADMM algorithm is derived in closed form and under the standard convex property to greatly speed up the convergence of ADMM-based distributed optimization. Using the Lyapunov direct approach, the proposed solution embeds control gains into a weighted network matrix among the agents uses and those weights as adaptive penalty gains in the augmented Lagrangian. For applications in a smart grid where system parameters are greatly affected by intermittent distributed energy resources like Electric Vehicles (EV) and Photo-voltaic (PV) panels, it is necessary to implement the algorithm in real-time since the accuracy of the optimal solution heavily relies on sampling time of the discrete-time iterative methods. Thus, the algorithm is further extended to the continuous domain for real-time applications and the convergence is proved also through Lyapunov direct approach. The algorithm is implemented on a distribution grid with high EV penetration where each agent exchanges relevant information among the neighboring nodes through the communication network, optimizes a combined convex objective of EV welfare and voltage regulation with power equations as constraints. The algorithm falls short when the dynamic equations like EVs state of charge are taken into account. Thus, the algorithm is further developed to incorporate dynamic constraints and the convergence along with control law is developed using Lyapunov direct approach. An alternative approach for convergence using passivity-short properties is also shown. Simulation results are included to demonstrate the effectiveness of proposed schemes
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more
Online Optimization of LTI Systems Under Persistent Attacks: Stability, Tracking, and Robustness
We study the stability properties of the interconnection of an LTI dynamical
plant and a feedback controller that generates control signals that are
compromised by a malicious attacker. We consider two classes of controllers: a
static output-feedback controller, and a dynamical gradient-flow controller
that seeks to steer the output of the plant towards the solution of a convex
optimization problem. We analyze the stability of the closed-loop system under
a class of switching attacks that persistently modify the control inputs
generated by the controllers. The stability analysis leverages the framework of
hybrid dynamical systems, Lyapunov-based arguments for switching systems with
unstable modes, and singular perturbation theory. Our results reveal that under
a suitable time-scale separation, the stability of the interconnected system
can be preserved when the attack occurs with "sufficiently low frequency" in
any bounded time interval. We present simulation results in a power-grid
example that corroborate the technical findings
Fuelling the zero-emissions road freight of the future: routing of mobile fuellers
The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios