scholarly journals Certifying Global Optimality for the L∞-Norm Computation of Large-Scale Descriptor Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 4279-4284
Author(s):  
P. Schwerdtner ◽  
E. Mengi ◽  
M. Voigt
Author(s):  
Alexander Murray ◽  
Timm Faulwasser ◽  
Veit Hagenmeyer ◽  
Mario E. Villanueva ◽  
Boris Houska

AbstractThis paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.


Energies ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3813 ◽  
Author(s):  
Yelena Vardanyan ◽  
Henrik Madsen

Gradually replacing fossil-fueled vehicles in the transport sector with Electric Vehicles (EVs) may help ensure a sustainable future. With regard to the charging electric load of EVs, optimal scheduling of EV batteries, controlled by an aggregating agent, may provide flexibility and increase system efficiency. This work proposes a stochastic bilevel optimization problem based on the Stackelberg game to create price incentives that generate optimal trading plans for an EV aggregator in day-ahead, intra-day and real-time markets. The upper level represents the profit maximizer EV aggregator who participates in three sequential markets and is called a Stackelberg leader, while the second level represents the EV owner who aims at minimizing the EV charging cost, and who is called a Stackelberg follower. This formulation determines endogenously the profit-maximizing price levels constraint by cost-minimizing EV charging plans. To solve the proposed stochastic bilevel program, the second level is replaced by its optimality conditions. The strong duality theorem is deployed to substitute the complementary slackness condition. The final model is a stochastic convex problem which can be solved efficiently to determine the global optimality. Illustrative results are reported based on a small case with two vehicles. The numerical results rely on applying the proposed methodology to a large scale fleet of 100, 500, 1000 vehicles, which provides insights into the computational tractability of the current formulation.


2017 ◽  
Vol 19 (3) ◽  
pp. 1217-1227 ◽  
Author(s):  
Khawaja Shafiq Haider ◽  
Abdul Ghafoor ◽  
Muhammad Imran ◽  
Fahad Mumtaz Malik

2013 ◽  
Vol 62 (5) ◽  
pp. 2253-2263 ◽  
Author(s):  
Yanhua Li ◽  
Abedelaziz Mohaisen ◽  
Zhi-Li Zhang

Opportunistic routing utilizes the broadcast nature of wireless networks, significantly promoting the unicast throughput. Many variations of opportunistic routing designs have been proposed, although all of the current designs consistently rely on all of the topology information to construct forwarder lists and process data forwarding, which indeed restricts the application in large-scale wireless networks, where collecting global optimal information is very costly. In this paper, we propose the localized opportunistic routing (LOR) protocol, which utilizes the distributed minimum transmission selection (MTS-B) algorithm to partition the topology into several nested close-node-sets (CNSs) using local information. LOR can locally realize the optimal opportunistic routing for a large-scale wireless network with low control overhead cost. Since it does not use global topology information, LOR highlights an interesting tradeoff between the global optimality of the used forwarder lists and scalability inferred from the incurred overhead. Extensive simulation results show that LOR dramatically improves performances over extremely opportunistic routing (ExOR) and MAC-independent opportunistic routing protocol (MORE), which are two well-known designs from the literature, in terms of control overhead, end-to-end delay, and throughputs. It also exhibits promising performance in vehicular ad hoc networks (VANETs).


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