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HYPERSPECTRAL SUPER-RESOLUTION VIA LOW RANK TENSOR TRIPLE DECOMPOSITION

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2024年第3期20卷 942-966页

作者： Cui, Xiaofei Chang, Jingya Guangdong Univ Technol Sch Math & Stat Guangzhou Peoples R China

Hyperspectral image (HSI) and multispectral image (MSI) fusion aims at producing a super-resolution image (SRI). In this paper, we establish a nonconvex optimization model for image fusion problem through low rank tensor triple decomposition. Using the limited memory BFGS (L-BFGS) approach, we develop a first-order optimization algorithm for obtaining the desired super-resolution image (TTDSR). Furthermore, two detailed methods are provided for calculating the gradient of the objective function. With the aid of the KurdykaLojasiewicz property, the iterative sequence is proved to converge to a stationary point. Finally, experimental results on different datasets show the effectiveness of our proposed approach.

关键词： Key words and phrases. Tensor triple decomposition nonconvex programming Kurdyka-Lojasiewicz property image fusion hyperspectral image multispectral image

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OPTIMAL COVERAGE OF CONVEX REGIONS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1986年第2期51卷 321-343页

作者： RUBINSTEIN, RY SAMORODNITSKY, G 1.Faculty of Industrial and Management Engineering Technion Haifa Israel

The problem of the coverage of convex regions with polygons and quadratic configurations of minimal volume is considered. The regions are presented as inequality constraints of a linear or nonlinear programming problem. It is shown that the problem of the optimal coverage with an arbitrary polygon can be reduced to a convex one of coverage with a multidimensional rectangle. If, however, rotation of the coordinate system is allowed, an additional nonconvex problem must be solved. It is also shown that, to find the minimal covering hypersphere or hyperellipsoid, one has to solve two convex programming problems. Algorithms and examples illustrating the feasibility of the proposed methods are presented.

关键词： Coverage problems convex hulls Monte Carlo optimization nonconvex programming

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Optimal Control of Switching Topology Networks

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MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-9页

作者： Mojica-Nava, Eduardo Salgado, Jimmy Tellez, Duvan Lopez, Alvaro Univ Nacl Colombia Dept Elect & Elect Engn Bogota Colombia Univ Los Andes Dept Ingn Elect & Elect Bogota Colombia Univ Catolica Colombia Programa Ingn Elect & Telecomunicac Bogota Colombia

We present an extension of a previously proposed approach based on the method of moments for solving the optimal control problem for a switching system considering now a continuous external input. This method is based on the transformation of a nonlinear, nonconvex optimal control problem, into an equivalent optimal control problem with linear and convex structure, which allows us to obtain an equivalent convex formulation more appropriate to be solved by high-performance numerical computing. Finally, the design of optimal logic-based controllers for networked systems with a dynamic topology is presented as an application of this work.

关键词： OPTIMAL control theory SWITCHING theory TOPOLOGY nonconvex programming NUMERICAL analysis

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Monotonic optimization for sensor cover energy problem

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OPTIMIZATION LETTERS 2018年第7期12卷 1569-1587页

作者： Pham Thi Hoai Hoang Tuy Hanoi Univ Sci & Technol Sch Appl Math & Informat 1 Dai Co Viet Hanoi Vietnam Inst Math 18 Hoang Quoc Viet Rd Hanoi Vietnam

We study the sensor cover energy problem (SCEP) in wireless communicationa difficult nonconvex problem with nonconvex constraints. A local approach based on DC programming called DCA was proposed by Astorino and Miglionico (Optim Lett 10(2):355-368, 2016) for solving this problem. In the present paper, we propose a global approach to (SCEP) based on the theory of monotonic optimization. By using an appropriate reformulation of (SCEP) we propose an algorithm for finding quickly a local optimal solution along with an efficient algorithm for computing a global optimal solution. Computational experiments are reported which demonstrate the practicability of the approach.

关键词： Wireless sensor networks Sensor coverage problem Monotonic optimization nonconvex programming

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Lossless convexification of nonconvex MINLP on the UAV path-planning problem

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OPTIMAL CONTROL APPLICATIONS & METHODS 2018年第2期39卷 845-859页

作者： Zhang, Zhe Wang, Jun Li, Jianxun Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Dept Automat 800 Dong Chuan Rd Shanghai 200240 Peoples R China Luoyang Elect Equipment Test Ctr China Luoyang Peoples R China

Most unmanned aerial vehicle path-planning problems have been modeled as linear optimal control problems, ie, as mixed-integer linear programming problems. However, most constraints cannot be described accurately in linear form in practical engineering applications. In this paper, the traditional unmanned aerial vehicle path-planning problem is modified as a nonconvex mixed-integer nonlinear programming problem, whose continuous relaxation is a nonconvex programming problem. A lossless convexification method is introduced into the generalized Benders decomposition algorithm framework. Thus, an optimal solution can be obtained without directly solving the nonconvex programming problem. The output of the proposed algorithm has been rigorously proved to be the optimal solution to the original problem. Meanwhile, the simulation results verify the validity of the theoretical analysis and demonstrate the superior efficiency of the proposed algorithm.

关键词： GBD lossless convexification MINLP nonconvex programming UAV path planning

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Duality and sensitivity in nonconvex quadratic optimization over an ellipsoid

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1996年第1期94卷 167-178页

作者： Flippo, OE Jansen, B CQN BV NL-5600 AK EINDHOVENNETHERLANDS UNIV LIMBURG FAC ECONNL-6200 MD MAASTRICHTNETHERLANDS

In this paper a duality framework is discussed for the problem of optimizing a nonconvex quadratic function over an ellipsoid. Additional insight is obtained from the observation that this nonconvex problem is in a sense equivalent to a convex problem of the same type, from which known necessary and sufficient conditions for optimality readily follow. Based on the duality results, some existing solution procedures are interpreted as in fact solving the dual. The duality relations are also shown to provide a natural framework for sensitivity analysis.

关键词： duality nonconvex programming quadratic programming sensitivity analysis trust region subproblem

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Waveform design for multiple extended targets in temporally correlated cognitive radar system

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IET RADAR SONAR AND NAVIGATION 2016年第2期10卷 398-410页

作者： Chen, Peng Wu, Lenan Southeast Univ Sch Informat Sci & Engn Nanjing 210096 Jiangsu Peoples R China Columbia Univ Dept Elect Engn New York NY 10027 USA

In cognitive radar systems, a closed-loop feedback is formed by the transmitter, environment, and receiver. Then, the transmit waveform can be optimised to improve the radar estimation performance. Unlike existing works that only consider single target with temporally correlated characteristic, waveform design for multiple extended targets is investigated in this study. The authors propose a Kalman filtering (KF)-based method to exploit the temporal correlation of target scattering coefficients (TSCs) and improve the corresponding estimation performance. Additionally, for the targets of both closed and separated in range, a novel optimisation problem is established to design the transmit waveform and minimise the mean square error of estimated TSC at each KF iteration, where an additional weight vector is introduced to achieve a trade-off among different targets. Since the optimisation problem is non-convex and cannot be solved efficiently, a two-step method is proposed to convert it into a convex problem, which can be solved by an optimisation toolbox such as CVX. Simulation results demonstrate that the joint method of waveform design outperforms the existing methods in TSC estimation for both separated and closed targets, and offers much more flexibility.

关键词： correlation theory waveform analysis radar receivers radar transmitters Kalman filters electromagnetic wave scattering mean square error methods minimisation concave programming iterative methods feedback multiple extended target temporally correlated cognitive radar system waveform design closed loop feedback transmitter receiver waveform transmission radar estimation performance Kalman filtering target scattering coefficients TSC estimation optimisation problem mean square error minimisation KF iteration weight vector CVX nonconvex programming

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GLOBAL MINIMIZATION BY REDUCING THE DUALITY GAP

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MATHEMATICAL programming 1994年第2期63卷 193-212页

作者： BENTAL, A EIGER, G GERSHOVITZ, V 1. Faculty of Industrial Engineering and Management Technion—Israel Institute of Technology 32000 Haifa Israel

We derive a general principle demonstrating that by partitioning the feasible set, the duality gap, existing between a nonconvex program and its lagrangian dual, can be reduced, and in important special cases, even eliminated. The principle can be implemented in a Branch and Bound algorithm which computes an approximate global solution and a corresponding lower bound on the global optimal value. The algorithm involves decomposition and a nonsmooth local search. Numerical results for applying the algorithm to the pooling problem in oil refineries are given.

关键词： GLOBAL OPTIMIZATION nonconvex programming DUALITY GAP BRANCH AND BOUND METHOD DECOMPOSITION NONSMOOTH OPTIMIZATION POOLING PROBLEM

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Canonical Duality for Box Constrained nonconvex and Nonsmooth Optimization Problems

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MATHEMATICAL PROBLEMS IN ENGINEERING 2015年第1期2015卷 1-9页

作者： Liu, Jing Liu, Huicheng Wuyi Univ Dept Math & Computat Sci Jiangmen 529020 Guangdong Peoples R China

This paper presents an application of the canonical duality theory for box constrained nonconvex and nonsmooth optimization problems. By use of the canonical dual transformation method, which is developed recently, these very difficult constrained optimization problems in R-n can be converted into the canonical dual problems, which can be solved by deterministic methods. The global and local extrema can be identified by the triality theory. Some examples are listed to illustrate the applications of the theory presented in the paper.

关键词： DUALITY theory (Mathematics) nonconvex programming NONSMOOTH optimization PROBLEM solving MATHEMATICAL analysis

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A Hybrid Evolutionary-Deterministic Optimization Approach for Conceptual Design

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INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2015年第41期54卷 10054-10072页

作者： Skiborowski, Mirko Rautenberg, Marcel Marquardt, Wolfgang Rhein Westfal TH Aachen AVT Proc Syst Engn D-52064 Aachen Germany

Most optimization-based approaches in conceptual, process design either focus on global optimization using simplified process models or utilize some kind of metaheuristic to optimize by means of repetitive runs of a detailed simulation model. Because the design of even a single distillation column model results in a nonconvex large-scale and mixed-integer optimization problem, if rigorous thermodynamic models are applied, deterministic optimization is still mostly limited to local optimization. In order to investigate and improve the solution quality of previously developed efficient local optimization approaches, this paper proposes a hybrid evolutionary deterministic optimization approach. The resulting memetic algorithm not only allows the optimization of the initial process structure but also facilitates discrete decision making that severely complicates a deterministic optimization due to the resulting discontinuities. The proposed approach not only eases the application by reducing the necessary user input for the initialization but also strengthens the confidence in the quality of the results because it provides an extensive screening of the design space. Several case studies, including utility and entrainer selection, demonstrate the performance of the hybrid optimization approach and suggest that even more complex design problems can be solved efficiently.

关键词： GLOBAL optimization METAHEURISTIC algorithms SIMULATION methods & models nonconvex programming THERMODYNAMICS DECISION making

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