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Subspace-Modeling-Based Nonlinear Measurement for Process Design

INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2011年第23期50卷 13457-13465页

作者： Lu, XinJiang Huang, MingHui Li, YiBo Chen, Min Cent S Univ State Key Lab High Performance Complex Mfg Changsha 410083 Hunan Peoples R China

In industry, many nonlinear processes can be approximated well by a linear model under a suitable design parameter, upon which a linear controller can effectively control these processes. The key problem is how to find this suitable design parameter, which is never considered in process design. In this paper, a novel design for control approach is proposed to design the process to have a satisfactory linear approximation. First, a subspace-modeling-based nonlinear measurement is proposed to avoid the infinite dimensional optimization problem in the traditional nonlinearity measurement. Then a particle-swarm-optimization-based design approach is developed to obtain the optimal design parameter through solving the nonconvex and nondifferential measurement problem. Finally, the proposed design is applied to design a practical curing oven and compared with the existing design.

关键词： PARTICLE swarm optimization MATHEMATICAL models MATHEMATICAL optimization EXPERIMENTAL design PROBLEM solving nonconvex programming NONLINEAR programming

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A note on the complexity of L_p minimization

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MATHEMATICAL programming 2011年第2期129卷 285-299页

作者： Ge, Dongdong Jiang, Xiaoye Ye, Yinyu Shanghai Jiao Tong Univ Antai Sch Econ & Management Shanghai 200052 Peoples R China Stanford Univ Inst Computat & Math Engn Stanford CA 94305 USA Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA

We discuss the L-p (0 <= p < 1) minimization problem arising from sparse solution construction and compressed sensing. For any fixed 0 < p < 1, we prove that finding the global minimal value of the problem is strongly NP-Hard, but computing a local minimizer of the problem can be done in polynomial time. We also develop an interior-point potential reduction algorithm with a provable complexity bound and demonstrate preliminary computational results of effectiveness of the algorithm.

关键词： nonconvex programming Global optimization Interior-point method Sparse solution reconstruction

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Inexact Proximal Point Methods in Metric Spaces

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SET-VALUED AND VARIATIONAL ANALYSIS 2011年第4期19卷 589-608页

作者： Zaslavski, Alexander J. Technion Israel Inst Technol Dept Math IL-32000 Haifa Israel

We study the local convergence of a proximal point method in a metric space under the presence of computational errors. We show that the proximal point method generates a good approximate solution if the sequence of computational errors is bounded from above by some constant. The principle assumption is a local error bound condition which relates the growth of an objective function to the distance to the set of minimizers introduced by Hager and Zhang (SIAM J Control Optim 46:1683-1704, 2007).

关键词： Computational error Metric space nonconvex programming Proximal method Well-posed problem

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Some Issues of Search of Extremal Processes in nonconvex Problems of Optimal Control

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AUTOMATION AND REMOTE CONTROL 2011年第6期72卷 1271-1281页

作者： Srochko, V. A. Rozinova, N. S. Irkutsk State Univ Irkutsk 664003 Russia

Problems of control are considered, for which the maximum principle releases extremal modes and points of the set of accessibility without optimality guaranty. In the framework of technology of the confidence region and on the basis of modified optimality criteria, some approaches to the problem of search for and improvement of extremal controls are presented.

关键词： nonconvex programming CONTROL theory (Mathematics) LINEAR systems NONLINEAR models (Statistics) CONFIDENCE intervals MATHEMATICAL optimization

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Aggregate Constraint Homotopy Method for Nonlinear programming on Unbounded Set

Aggregate Constraint Homotopy Method for Nonlinear Programmi...

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International Conference on Intelligent Structure and Vibration Control (ISVC 2011)

作者： Xiao Yu Xiong Huijuan Yan Zhigang E China Jiaotong Univ Sch Basic Sci Nanchang 330013 Jiangxi Peoples R China Huazhong Agr Univ Dept Sci Wuhan 430070 Peoples R China Dongbei Univ Finance & Econ Accountancy Coll Dalian 116025 Peoples R China

ISBN: (纸本)9783037850206

In [1], an aggregate constraint aggregate (ACH) method for nonconvex nonlinear programming problems was presented and global convergence result was obtained when the feasible set is bounded and satisfies a weak normal cone condition with some standard constraint qualifications. In this paper, without assuming the boundedness of feasible set, the global convergence of ACH method is proven under a suitable additional assumption.

关键词： nonlinear programming nonconvex programming unbounded set aggregate constraint homotopy method

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Linear Precoding Designs for Amplify-and-Forward Multiuser Two-Way Relay Systems

Linear Precoding Designs for Amplify-and-Forward Multiuser T...

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54th Annual IEEE Global Telecommunications Conference (GLOBECOM)

作者： Wang, Rui Tao, Meixia Shanghai Jiao Tong Univ Dept Elect Engn Shanghai 200240 Peoples R China

ISBN: (纸本)9781424492688

We investigate the linear precoding designs for multiuser two-way relay system (MU-TWRS) where a multi-antenna base-station (BS) communicates with multiple single-antenna mobile stations (MSs) via a multi-antenna relay station (RS). The amplify-and-forward (AF) relay protocol is employed. The design goal is to optimize the precodings at BS, RS or both so as to minimize the total mean-square error (MSE) of the uplink messages while maintaining the individual signal-to-interference-plus-noise ratio (SINR) requirement for each downlink signal. We show that the BS precoding design problem can be converted to a standard second order cone programming (SOCP), while the RS precoding is non-convex for which a local optimal solution is obtained using an iterative algorithm. A joint BS-RS precoding is also obtained by alternating optimization of BS precoding and RS precoding with guaranteed convergence. Numerical results show that RS-precoding is superior to BS-precoding. Furthermore, the joint BS-RS precoding can significantly outperform the two individual precoding schemes. The implementation issues including complexity and feedback overhead are also discussed.

关键词： BS-precoding Downlink Interference Joints Optimization RS-precoding Relays Signal to noise ratio Vectors amplify and forward communication amplify and forward protocol concave programming cone programming interference suppression iterative algorithm iterative methods linear codes linear precoding design mean square error method mean square error methods mobile stations multi-antenna base station multi-antenna relay station multifrequency antennas multiuser channels multiuser two-way relay system nonconvex programming optimization precoding protocols signal to interference plus noise ratio uplink messages

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A Deep-Cutting-Plane Technique for Reverse Convex Optimization

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS 2011年第4期41卷 1054-1060页

作者： Moshirvaziri, Khosrow Amouzegar, Mahyar A. Calif State Univ Long Beach Dept Informat Syst Long Beach CA 90840 USA RAND Corp Santa Monica CA 90401 USA

A large number of problems in engineering design and in many areas of social and physical sciences and technology lend themselves to particular instances of problems studied in this paper. Cutting-plane methods have traditionally been used as an effective tool in devising exact algorithms for solving convex and large-scale combinatorial optimization problems. Its utilization in nonconvex optimization has been also promising. A cutting plane, essentially a hyperplane defined by a linear inequality, can be used to effectively reduce the computational efforts in search of a global solution. Each cut is generated in order to eliminate a large portion of the search domain. Thus, a deep cut is intuitively superior in which it will exclude a larger set of extraneous points from consideration. This paper is concerned with the development of deep-cutting-plane techniques applied to reverse-convex programs. An upper bound and a lower bound for the optimal value are found, updated, and improved at each iteration. The algorithm terminates when the two bounds collapse or all the generated subdivisions have been fathomed. Finally, computational considerations and numerical results on a set of test problems are discussed. An illustrative example, walking through the steps of the algorithm and explaining the computational process, is presented.

关键词： Cutting-plane methods global optimization nonconvex programming reverse-convex programs (RCPs)

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Rheology of granular materials composed of nonconvex particles

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Physical Review E 2011年第4期84卷 041302-041302页

作者： B. Saint-Cyr J.-Y. Delenne C. Voivret F. Radjai P. Sornay LMGC CNRS-Université Montpellier 2 Place Eugène Bataillon F-34095 Montpellier cedex 05 France CEA DEN SPUA LCU F-13108 Saint Paul lez Durance France

By means of contact dynamics simulations, we investigate the shear strength and internal structure of granular materials composed of two-dimensional nonconvex aggregates. We find that the packing fraction first grows as the nonconvexity is increased but declines at higher nonconvexity. This unmonotonic dependence reflects the competing effects of pore size reduction between convex borders of aggregates and gain in porosity at the nonconvex borders that are captured in a simple model fitting nicely the simulation data both in the isotropic and sheared packings. On the other hand, the internal angle of friction increases linearly with nonconvexity and saturates to a value independent of nonconvexity. We show that fabric anisotropy, force anisotropy, and friction mobilization, all enhanced by multiple contacts between aggregates, govern the observed increase of shear strength and its saturation with increasing nonconvexity. The main effect of interlocking is to dislocate frictional dissipation from the locked double and triple contacts between aggregates to the simple contacts between clusters of aggregates. This self-organization of particle motions allows the packing to keep a constant shear strength at high nonconvexity.

关键词： RHEOLOGY FRICTION GRANULAR materials PARTICLES (Nuclear physics) nonconvex programming

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Weak Subdifferential in Nonsmooth Analysis and Optimization

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JOURNAL OF APPLIED MATHEMATICS 2011年第unknown期2011卷 1-9页

作者： Meherrem, Sahlar F. Polat, Refet Yasar Univ Dept Math TR-35100 Izmir Turkey

Some properties of the weak subdifferential are considered in this paper. By using the definition and properties of the weak subdifferential which are described in the papers (Azimov and Gasimov, 1999;Kasimbeyli and Mammadov, 2009;Kasimbeyli and Inceoglu, 2010), the author proves some theorems connecting weak subdifferential in nonsmooth and nonconvex analysis. It is also obtained necessary optimality condition by using the weak subdifferential in this paper.

关键词： SUBDIFFERENTIALS NONSMOOTH optimization nonconvex programming MATHEMATICAL analysis PROOF theory CONVEX functions

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An inexact Newton method for nonconvex equality constrained optimization

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MATHEMATICAL programming 2010年第2期122卷 273-299页

作者： Byrd, Richard H. Curtis, Frank E. Nocedal, Jorge Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA Univ Colorado Dept Comp Sci Boulder CO 80309 USA Northwestern Univ Dept Elect Engn & Comp Sci Evanston IL 60208 USA

We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351-369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the presence of negative curvature without requiring information about the inertia of the primal-dual iteration matrix. Negative curvature may arise from second-order information of the problem functions, but in fact exact second derivatives are not required in the approach. The complete algorithm is characterized by its emphasis on sufficient reductions in a model of an exact penalty function. We analyze the global behavior of the algorithm and present numerical results on a collection of test problems.

关键词： Large-scale optimization Constrained optimization nonconvex programming Inexact linear system solvers Krylov subspace methods

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