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On a modified subgradient algorithm for dual problems via sharp augmented Lagrangian

JOURNAL OF GLOBAL OPTIMIZATION 2006年第1期34卷 55-78页

作者： Burachik, RS Gasimov, RN Ismayilova, NA Kaya, CY Univ Fed Rio de Janeiro COPPE BR-21941972 Rio de Janeiro Brazil Osmangazi Univ Dept Ind Engn TR-26030 Bademlik Eskisehir Turkey Univ S Australia Sch Math & Stat Mawson Lakes SA 5095 Australia

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem.

关键词： augmented Lagrangian nonconvex programming nonsmooth optimization sharp Lagrangian subgradient optimization

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DETERMINISTIC GLOBAL OPTIMIZATION WITH PARTITION SETS WHOSE FEASIBILITY IS NOT KNOWN - APPLICATION TO CONCAVE MINIMIZATION, REVERSE CONVEX CONSTRAINTS, DC-programming, AND LIPSCHITZIAN OPTIMIZATION

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1988年第1期58卷 11-37页

作者： HORST, R 1.Fachbereich IV-Mathematik Universit?t Trier Trier West Germany

A crucial problem for many global optimization methods is how to handle partition sets whose feasibility is not known. This problem is solved for broad classes of feasible sets including convex sets, sets defined by finitely many convex and reverse convex constraints, and sets defined by Lipschitzian inequalities. Moreover, a fairly general theory of bounding is presented and applied to concave objective functions, to functions representable as differences of two convex functions, and to Lipschitzian functions. The resulting algorithms allow one to solve any global optimization problem whose objective function is of one of these forms and whose feasible set belongs to one of the above classes. In this way, several new fields of optimization are opened to the application of global methods.

关键词： Global optimization nonconvex programming mathematical programming concave minimization DC-programming Lipschitzian optimization branch-and-bound methods

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Secrecy Rate Beamforming for Multicell Networks With Information and Energy Harvesting

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第3期65卷 677-689页

作者： Nasir, Ali Arshad Hoang Duong Tuan Duong, Trung Q. Poor, H. Vincent King Fahd Univ Petr & Minerals Dept Elect Engn Dhahran 31261 Saudi Arabia Univ Technol Sydney Fac Engn & Informat Technol Broadway NSW 2007 Australia Queens Univ Belfast Sch Elect Elect Engn & Comp Sci Belfast BT7 1NN Antrim North Ireland Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

Considering a multicell network for the secure wireless information and power transfer, this paper studies the joint design of transmit beamformers at the base stations (BSs) and receive signal splitting ratios at the end users' equipment (UE). The primary concern in this work is the network internal security, where there may be a single multiantenna eavesdropper or there is a risk that any near user may accidentally eavesdrop on the received signal of any far user. The objective is to maximize the minimum secrecy user rate under BS transmit power and UE minimum harvested energy constraints. New path-following algorithms are proposed for computational solutions of these difficult nonconvex optimization problems. Each iteration involves one simple convex quadratic program. Numerical results confirm that the proposed algorithms converge quickly after few iterations having a low computational complexity.

关键词： Secure communication secrecy rate energy harvesting nonconvex programming wireless information and power transfer signal splitting transmit beamforming

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A Branch-and-Reduce Approach for Solving Generalized Linear Multiplicative programming

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MATHEMATICAL PROBLEMS IN ENGINEERING 2011年第1期2011卷 1-12页

作者： Wang, Chun-Feng Liu, San-Yang Zheng, Geng-Zhong Xidian Univ Dept Math Sci Xian 710071 Peoples R China Henan Normal Univ Dept Math Xinxiang 453007 Peoples R China Xidian Univ Sch Comp Sci & Technol Xian 710071 Peoples R China

We consider a branch-and-reduce approach for solving generalized linear multiplicative programming. First, a new lower approximate linearization method is proposed;then, by using this linearization method, the initial nonconvex problem is reduced to a sequence of linear programming problems. Some techniques at improving the overall performance of this algorithm are presented. The proposed algorithm is proved to be convergent, and some experiments are provided to show the feasibility and efficiency of this algorithm.

关键词： COMPLEX multiplication nonconvex programming ALGORITHMS VECTOR analysis MATHEMATICAL programming

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A NEW ALGORITHM FOR SOLVING VARIATIONAL-INEQUALITIES WITH APPLICATION TO THE TRAFFIC ASSIGNMENT PROBLEM

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MATHEMATICAL programming 1985年第3期33卷 339-351页

作者： MARCOTTE, P 1.Centre de Recherche sur les Transports Université de Montréal Canada

The variational inequality problem in Euclidian space is formulated as a nonconvex, nondifferentiable optimization problem. We show that any stationary point is optimal, and we propose a solution algorithm that decreases the nondifferential objective monotonically. Application to the asymmetric traffic assignment problem is considered.

关键词： Variational Inequality Nondifferentiable Optimization nonconvex programming Network Optimization

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Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2008年第3期67卷 479-491页

作者： Gao, David Yang Ruan, Ning Virginia Polytech Inst & State Univ Dept Math Blacksburg VA 24061 USA Shanghai Univ Sci & Technol Sch Management Shanghai 200093 Peoples R China

This paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-dimensional space can be converted into an one-dimensional canonical dual problem with zero duality gap, which can be solved easily to obtain all dual solutions. Each dual solution leads to a primal solution. Both global and local extremality conditions of these primal solutions can be identified by the triality theory associated with the canonical duality theory. Several examples are illustrated.

关键词： duality theory nonconvex programming global optimization quadratic-exponential function nonlinear algebraic equation triality

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Task-Space Framework for Bilateral Teleoperation With Time Delays

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JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME 2012年第5期134卷 1-10页

作者： Wang, Hanlei Xie, Yongchun Beijing Inst Control Engn Sci & Technol Space Intelligent Control Lab Beijing 100190 Peoples R China

This paper investigates the task-space control framework for bilateral teleoperation with communication time delays. Teleoperation in task space R-3 x SO(3) presents some distinctive features different from its joint-space counterpart, i.e., SO(3) is nonconvex and bears quite different structure from Euclidean space R-n. Through analyzing the energy flows at the two ports of the teleoperator, we rigorously define the task-space interaction passivity of the teleoperator. Based on this passivity framework, we propose delay-robust control schemes to achieve master-slave position/orientation synchronization. Singularity-free task-space interaction passivity of the closed-loop teleoperator is ensured by the proposed task-space control framework. Using Lyapunov-Krasovskii stability tool and Schwarz inequality, we analyze the performance of the proposed teleoperation control scheme. We also discuss the problems incurred by time-varying delays and the corresponding solutions. Simulation study on a master-slave teleoperator composed of two kinematically dissimilar six-degree of freedom (DOF) manipulators is performed to illustrate the performance of the proposed control approach. [DOI: 10.1115/1.4006215]

关键词： REMOTE control TIME delay systems CONTROL theory (Mathematics) COMMUNICATION DEGREES of freedom nonconvex programming ROBUST control

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A Plant Propagation Algorithm for Constrained Engineering Optimisation Problems

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MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-10页

作者： Sulaiman, Muhammad Salhi, Abdellah Selamoglu, Birsen Irem Kirikchi, Omar Bahaaldin Univ Essex Dept Math Sci Colchester CO4 3SQ Essex England Abdul Wali Khan Univ Dept Math Mardan Kpk Pakistan

Optimisation problems arising in industry are some of the hardest, often because of the tight specifications of the products involved. They are almost invariably constrained and they involve highly nonlinear, and non-convex functions both in the objective and in the constraints. It is also often the case that the solutions required must be of high quality and obtained in realistic times. Although there are already a number of well performing optimisation algorithms for such problems, here we consider the novel Plant Propagation Algorithm (PPA) which on continuous problems seems to be very competitive. It is presented in a modified form to handle a selection of problems of interest. Comparative results obtained with PPA and state-of-the-art optimisation algorithms of the Nature-inspired type are presented and discussed. On this selection of problems, PPA is found to be as good as and in some cases superior to these algorithms.

关键词： PLANT propagation MATHEMATICAL optimization NONLINEAR theories nonconvex programming CONTINUOUS functions

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Secure and Energy-Efficient Beamforming for Simultaneous Information and Energy Transfer

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2017年第11期16卷 7523-7537页

作者： Nasir, Ali Arshad Hoang Duong Tuan Duong, Trung Q. Poor, H. Vincent King Fahd Univ Petr & Minerals Dept Elect Engn Dhahran Saudi Arabia Univ Technol Sydney Sch Elect & Data Engn Broadway NSW 2007 Australia Queens Univ Belfast Belfast BT7 1NN Antrim North Ireland Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

Some next-generation wireless networks will likely involve the energy-efficient transfer of information and energy over the same wireless channel. Moreover, densification of such networks will make the physical layer more vulnerable to cyber attacks by potential multi-antenna eavesdroppers. To address these issues, this paper considers transmit time-switching (TS) mode, in which energy and information signals are transmitted separately in time by the base station (BS). This protocol is not only easy to implement but also delivers the opportunity for multi-purpose beamforming, in which energy beamformers can be used to jam eavesdroppers during wireless power transfer. In the presence of imperfect channel estimation and multi-antenna eavesdroppers, the energy and information beamformers and the transmit TS ratio are jointly optimized to maximize the worst-case user secrecy rate subject to energy constrained users' harvested energy thresholds and a BS transmit power budget. New robust path-following algorithms, which involve one simple convex quadratic program at each iteration are proposed for computational solutions of this difficult optimization problem and also the problem of secure energy efficiency maximization. The latter adds further complexity due to additional optimization variables appearing in the denominator of the secrecy rate function. Numerical results confirm that the performance of the proposed computational solutions is robust against channel uncertainties.

关键词： Secrecy rate secrecy energy efficiency wireless power transfer time switching beamforming nonconvex programming

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ON THE CONVERGENCE OF CUTTING PLANE ALGORITHMS FOR A CLASS OF nonconvex MATHEMATICAL PROGRAMS

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MATHEMATICAL programming 1985年第1期31卷 42-56页

作者： SEN, S SHERALI, HD VIRGINIA POLYTECH INST & STATE UNIV DEPT IND ENGN & OPERAT RESBLACKSBURGVA 24061

We discuss the convergence of cutting plane algorithms for a class of nonconvex programs called the Generalized Lattice Point Problems (GLPP). A set of sufficient conditions which guarantee finite convergence are presented. Although these conditions are usually difficult to enforce in a practical implementation, they do illustrate the various factors that must be involved in a convergent rudimentary cutting plane algorithm. A striking example of nonconvergence (in which no subsequence converges to a feasible solution, even when seemingly strong cutting planes are used), is presented to show the effect of neglecting one such factor. We give an application of our analysis to problems with multiple choice constraints and finally discuss a modification of cutting plane algorithms so as to make finite convergence more readily implementable.

关键词： Convergence Cutting Planes nonconvex programming

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