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An active set algorithm for nonlinear optimization with polyhedral constraints

Science China Mathematics 2016年第8期59卷 1525-1542页

作者： HAGER William W. ZHANG Hongchao Department of Mathematics University of FloridaGainesvilleFL 32611-8105USA Department of Mathematics Louisiana State UniversityBaton RougeLA 70803-4918USA

A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.

关键词： polyhedral constrained optimization active set algorithm PASA gradient projection algorithm local and global convergence

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Triangular MIMO Relay Channels: Simultaneous Signal and Interference Alignment

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2015年第1期64卷 223-235页

作者： Teav, Keov Kolyan Zhou, Zhendong Vucetic, Branka Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia

In this paper, we propose a new three-user network information flow model, referred to as the triangular multiple-input-multiple-output (MIMO) relay (TMR) channel, which consists of three users and three relays equipped with n(U) and n(R) antennas, respectively. Each user sends two independent messages to the other two users via the adjacent relays in two time slots, which are referred to as the multiple-access and broadcast stages. We derive a novel simultaneous signal and interference alignment for the proposed TMR channel in a scenario where there are fewer antennas at each relay than at each user (n(R) < n(U)). An optimized pseudo-inverse scheme based on an efficient gradient projection algorithm is proposed to solve the simultaneous alignment problem. By deriving a gradient over weighted sum-rate maximization and applying a gradient descent method, the optimal beamforming vectors are obtained to maximize the effective signal-to-noise ratios. Furthermore, to obtain rapid convergence speed and reduce computational complexity, we introduce a quasi-Newton method, which is referred to as the Broyden-Fletcher-Goldfarb-Shanno algorithm, by approximating the Hessian matrix of a pure Newton method. The convergence of the proposed gradient algorithm is guaranteed by proposing a line search algorithm. Finally, a performance evaluation shows that the proposed scheme offers a higher sum rate, produces a better outage probability, and achieves a higher multiplexing gain than the existing schemes.

关键词： Beamforming optimization gradient projection algorithm interference alignment multiple-input-multipleoutput (MIMO) relay channel

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Dual optimization design in formation keeping trajectory of multi UAV 34

Dual optimization design in formation keeping trajectory of ...

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第三十四届中国控制会议

作者： WANG Jian-hong ZHU Yong-hong School of Mechanical and Electronic Engineering Jingdezhen Ceramic Institute

ISBN: (纸本)9781467374439

When considering the problem of how to design multi UAV formation keeping optimization model, we combine the kinematic equation of multi UAV, performance index and constrained condition to construct a constrained optimization problem. After some transformation is used in the performance function to decompose the optimization problem, we introduce the Lagrange multiplier vector to construct a Lagrange function of this constrained optimization problem. To obtain the two classes of optimization variables-primal variable and dual variable, we find that all primal variables and dual variables can be formulated to the expressions about one dual variable. Then the gradient projection method from the convex optimization theory is proposed to obtain this dual variable. When this dual variable is solved, all the other optimization variables can also be obtained through simple substitution Finally, the efficiency of the proposed strategy can be confirmed by the simulation results.

关键词： multi UAV formation keeping dual optimization gradient projection algorithm

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Theory and Practice in Large Carpooling Problems

Theory and Practice in Large Carpooling Problems

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5th International Conference on Ambient Systems, Networks and Technologies (ANT) / 4th International Conference on Sustainable Energy Information Technology (SEIT)

作者： Hartman, Irith Ben-Arroyo Keren, Daniel Abu Dbai, Abed Cohen, Elad Knapen, Luk Yasar, Ansar-Ul-Haque Janssens, Davy Univ Haifa Dept Comp Sci IL-3498838 Haifa Israel Univ Haifa Caesarea Rothschild Inst IL-3498838 Haifa Israel Hasselt Univ Transportat Res Inst IMOB B-3950 Diepenbeek Belgium

We address the carpooling problem as a graph-theoretic problem. If the set of drivers is known in advance, then for any car capacity, the problem is equivalent to the assignment problem in bipartite graphs. Otherwise, when we do not know in advance who will drive their vehicle and who will be a passenger, the problem is NP-hard. We devise and implement quick heuristics for both cases, based on graph algorithms, as well as parallel algorithms based on geometric/algebraic approach. We compare between the algorithms on random graphs, as well as on real, very large, data. (C) 2014 Published by Elsevier B.V.

关键词： Carpooling Linear Programming Maximum Weighted Matching Star Partition Problem gradient projection algorithm Scalability Incremental algorithms

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A Minimum Delay Link Scheduling algorithm in Vehicular Ad-Hoc Networks 2

A Minimum Delay Link Scheduling Algorithm in Vehicular Ad-Ho...

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2nd IEEE International Conference on Progress in Informatics and Computing (PIC)

作者： Zhang, Yong Wang, Junyi Lin, Jiming Guilin Univ Elect Technol Minist Educ Key Lab Cognit Radio & Informat Proc Guilin 541004 Peoples R China Guilin Univ Elect Technol Guangxi Expt Ctr Informat Sci Guilin 541004 Peoples R China

ISBN: (纸本)9781479920303

Reducing the information transmission delay in the Vehicular Ad Hoc Networks(VANETs) can improve the timeliness of receiving information and avoid the happening of the accident. As a potential solution, cooperative transmission, which may effectively reduce the transmission delay by exploiting spatial diversity, has attracted lots of attentions recently. In this paper, we modeled the information transmission delay minimization of the VANETs in which cooperative transmission is allowed, and proposed a gradient projection algorithm based on the model. The RSU can schedule the vehicle transmission behavior according to the algorithm, so as to solve the problem of the information transmission delay minimization in the VANETs where multipath routings(MRTDM) are considered. Finally, our simulation results show that the algorithm not only has good convergence, but also can solve the MRTDM in VANETs.

关键词： vehicular ad-hoc networks cooperative transmission gradient projection algorithm delay minimization

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Theory and Practice in Large Carpooling Problems

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Procedia Computer Science 2014年 32卷 339-347页

作者： Irith Ben-Arroyo Hartman Daniel Keren Abed Abu Dbai Elad Cohen Luk Knapen Ansar-Ul-Haque Yasar Davy Janssens Department of Computer Science University of Haifa Haifa 3498838 Israel Caesarea Rothschild Institute University of Haifa Haifa 3498838 Israel Transportation Research Institute(IMOB) Hasselt University Wetenschapspark 5 B3950 Diepenbeek Belgium

关键词： Carpooling Linear Programming Maximum Weighted Matching Star Partition Problem gradient projection algorithm Scalability Incremental algorithms

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The hybrid steepest descent method for solutions of equilibrium problems and other problems in fixed point theory

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FIXED POINT THEORY AND APPLICATIONS 2014年第1期2014卷 156-156页

作者： Osilike, Micha O. Ofoedu, Eric U. Attah, Felix U. Univ Nigeria Dept Math Nsukka Nigeria Nnamdi Azikiwe Univ Dept Math Awka Nigeria Akanu Ibiam Fed Polytech Dept Maths Stat Unwana Nigeria

In this paper, we combine the gradient projection algorithm and the hybrid steepest descent method and prove the strong convergence to a common element of the equilibrium problem;the null space of an inverse strongly monotone operator;the set of fixed points of a continuous pseudocontractive mapping and the minimizer of a convex function. This common element is proved to be the unique solution of a variational inequality problem.

关键词： steepest descent method monotone equilibrium problems gradient projection algorithm pseudocontractive mapping variational inequality

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A Minimum Delay Link Scheduling algorithm in Vehicular Ad-Hoc Networks

A Minimum Delay Link Scheduling Algorithm in Vehicular Ad-Ho...

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2014 IEEE International Conference on Progress in Informatics and Computing

作者： Yong Zhang Junyi Wang Jiming Lin Key Laboratory of Cognitive Radioand Information Processing Ministry of EducationGuilin University of Electronic Technology Guangxi Experiment Center of Information Science Guilin University of Electronic Technology

Reducing the information transmission delay in the Vehicular Ad Hoc Networks(VANETs) can improve the timeliness of receiving information and avoid the happening of the accident. As a potential solution, cooperative transmission,which may effectively reduce the transmission delay by exploiting spatial diversity, has attracted lots of attentions recently. In this paper, we modeled the information transmission delay minimization of the VANETs in which cooperative transmission is allowed, and proposed a gradient projection algorithm based on the model. The RSU can schedule the vehicle transmission behavior according tothe algorithm, soas tosolve the problem of the information transmission delay minimization in the VANETs where multipath routings(MRTDM) are ***, our simulation results show that the algorithm not only has good convergence, but alsocan solve the MRTDM in VANETs.

关键词： vehicular ad-hoc networks cooperative transmission gradient projection algorithm delay minimization

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A Model-Free No-arbitrage Price Bound for Variance Options

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APPLIED MATHEMATICS AND OPTIMIZATION 2013年第1期68卷 43-73页

作者： Bonnans, J. Frederic Tan, Xiaolu Ecole Polytech INRIA Saclay F-75230 Paris France Ecole Polytech CMAP F-75230 Paris France

We suggest a numerical approximation for an optimization problem, motivated by its applications in finance to find the model-free no-arbitrage bound of variance options given the marginal distributions of the underlying asset. A first approximation restricts the computation to a bounded domain. Then we propose a gradient projection algorithm together with the finite difference scheme to solve the optimization problem. We prove the general convergence, and derive some convergence rate estimates. Finally, we give some numerical examples to test the efficiency of the algorithm.

关键词： Variance option Model-free price bound gradient projection algorithm

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OPTIMAL TRANSPORTATION UNDER CONTROLLED STOCHASTIC DYNAMICS

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ANNALS OF PROBABILITY 2013年第5期41卷 3201-3240页

作者： Tan, Xiaolu Touzi, Nizar Ecole Polytech CMAP F-91128 Palaiseau France

We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the continuous semimartingale. The optimal transportation problem minimizes the cost among all continuous semimartingales with given initial and terminal distributions. Our first main result is an extension of the Kantorovitch duality to this context. We also suggest a finite-difference scheme combined with the gradient projection algorithm to approximate the dual value. We prove the convergence of the scheme, and we derive a rate of convergence. We finally provide an application in the context of financial mathematics, which originally motivated our extension of the Monge-Kantorovitch problem. Namely, we implement our scheme to approximate no-arbitrage bounds on the prices of exotic options given the implied volatility curve of some maturity.

关键词： Mass transportation Kantorovitch duality viscosity solutions gradient projection algorithm

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