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concave programming for finding sparse solutions to problems with convex constraints

OPTIMIZATION METHODS & SOFTWARE 2011年第6期26卷 971-992页

作者： Rinaldi, F. Univ Roma La Sapienza Dipartimento Informat & Sistemist I-00185 Rome Italy

In this work, we consider a class of nonlinear optimization problems with convex constraints with the aim of computing sparse solutions. This is an important task arising in various fields such as machine learning, signal processing, and data analysis. We adopt a concave optimization-based approach, we define an effective version of the Frank-Wolfe algorithm, and we prove the global convergence of the method. Finally, we report numerical results on test problems showing both the effectiveness of the concave approach and the efficiency of the implemented algorithm.

关键词： zero-norm concave programming Frank-Wolfe method

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The static output feedback stabilization problem as a concave-convex programming problem

The static output feedback stabilization problem as a concav...

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American Control Conference

作者： Astolfi, A Colaneri, P Univ London Imperial Coll Sci Technol & Med Dept Elect Engn London SW7 2AZ England

ISBN: (纸本)0780383354

It is shown that the static output feedback stabilization problem for linear multi-input single-output (MISO) systems can be posed as a concave-convex programming problem. This allows the potential design of minimization algorithms yielding a stabilizing static output feedback gain, if it exists, or showing that the problem is not solvable at all.

关键词： feedback stability concave programming convex programming multivariable control systems minimisation static output feedback stabilization concave convex programming problem linear multiinput single output system minimization algorithm

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A concave optimization-based approach for sparse multiobjective programming

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OPTIMIZATION LETTERS 2020年第3期14卷 535-556页

作者： Cocchi, Guido Levato, Tommaso Liuzzi, Giampaolo Sciandrone, Marco Univ Firenze Dipartimento Ingn Informaz Via Santa Marta 3 I-50139 Florence Italy CNR Ist Anal Sistemi & Informat Via Taurini 19 I-00185 Rome Italy

The paper is concerned with multiobjective sparse optimization problems, i.e. the problem of simultaneously optimizing several objective functions and where one of these functions is the number of the non-zero components (or the 0-norm) of the solution. We propose to deal with the 0-norm by means of concave approximations depending on a smoothing parameter. We state some equivalence results between the original nonsmooth problem and the smooth approximated problem. We are thus able to define an algorithm aimed to find sparse solutions and based on the steepest descent framework for smoothmultiobjective optimization. The numerical results obtained on a classical application in portfolio selection and comparison with existing codes show the effectiveness of the proposed approach.

关键词： Multiple objective programming Sparse optimization concave programming Multiobjective steepest descent methods

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A continuous approach for the concave cost supply problem via DC programming and DCA

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DISCRETE APPLIED MATHEMATICS 2008年第3期156卷 325-338页

作者： Le Thi, Hoai An Dinh, Tao Pham Univ Metz Lab Theoret & Appl Comp Sci UFR MIM F-57045 Metz France Natl Inst Appl Sci Lab Modelling Optimizat & Operat Res F-76131 Mont St Aignan France

The paper addresses an important but difficult class of concave cost supply management problems which consist in minimizing a separable increasing concave objective function subject to linear and disjunctive constraints. We first recast these problems into mixed zero-one nondifferentiable concave minimization over linear constraints problems and then apply exact penalty techniques to state equivalent nondifferentiable polyhedral DC (Difference of Convex functions) programs. A new deterministic approach based on DC programming and DCA (DC Algorithms) is investigated to solve the latter ones. Finally numerical simulations are reported which show the efficiency, the robustness and the globality of our approach. (c) 2007 Elsevier B.V. All fights reserved.

关键词： reformulation concave cost supply problem disjunctive constraints mixed 0-1 concave programming exact penalty concave programming DC (Difference of convex functions) programming DCA

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Continuous Piecewise Linear programming via concave Optimization and Genetic Algorithm

Continuous Piecewise Linear Programming via Concave Optimiza...

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51st IEEE Annual Conference on Decision and Control (CDC)

作者： Xi, Xiangming Xu, Jun Mu, Xiaomu Wang, Shuning Tsinghua Univ Tsinghua Natl Lab Informat Sci & Technol Dept Automat Beijing 100084 Peoples R China China Univ Petr Fac Res Inst Automat Beijing 102249 Peoples R China

ISBN: (纸本)9781467320665

This paper describes continuous piecewise linear (CPWL) programming where the objective and constraints are in the form of hinging hyperplane (HH). And HH has received wide attention due to its simplicity and good performance in system identification. When solving a CPWL programming problem, some excellent features inspire us to come up with more efficient algorithms: the two distinguished states of a hinge function reminds us of application of genetic algorithm, while the piecewise linearity and concavity of the problem of minimization of HH naturally lead to the usage of well developed methods for concave programming, such as the cutting plane method. In order to find the global minima, we propose an improved genetic algorithm (GA) incorporating the cutting plane method. The main improvement lies in three aspects. First, it utilizes binary strings that derive local minima as chromosomes, with the proposed local minima locating method. Second, a stopping criterion has been established to ensure the global optimality of GA, with the structure information provided by gamma extension of local minima. And third, genetic operations have also been revised to enhance the performance of the algorithm, which is assessed by the computational experiments.

关键词： concave programming genetic algorithms linear programming minimisation piecewise linear techniques

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Outlier detection of multivariate data via the maximization of the cumulant generating function

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2025年 461卷

作者： Cesarone, Francesco Giacometti, Rosella Ricci, Jacopo Maria Roma Tre Univ Dept Business Studies Rome Italy Univ Bergamo Dept Management Bergamo Italy

In this paper, we propose an outlier detection algorithm for multivariate data based on their projections on the directions that maximize the Cumulant Generating Function (CGF). We prove that CGF is a convex function, and we characterize the CGF maximization problem on the unit ncircle as a concave minimization problem. Then, we show that the CGF maximization approach can be interpreted as an extension of the standard principal component technique. Therefore, for validation and testing, we provide a thorough comparison of our methodology with two other projection-based approaches both on artificial and real-world financial data. Finally, we apply our method as an early detector for financial crises.

关键词： Outlier detection Cumulant generating function Principal component analysis Projections Multivariate skew-normal distribution concave programming

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Near-optimal hybrid precoding for millimeter wave massive MIMO systems via cost-efficient Sub-connected structure

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IET COMMUNICATIONS 2020年第14期14卷 2340-2349页

作者： Huang, Yu Liu, Chen Song, Yunchao Yu, Xiaolei Nanjing Univ Posts & Telecommun Coll Elect & Opt Engn Nanjing Peoples R China Nanjing Univ Posts & Telecommun Coll Microelect Nanjing Peoples R China Nanjing Univ Posts & Telecommun Natl & Local Joint Engn Lab RF Integrat & Microas Nanjing Peoples R China Jiangsu Inst Qual & Standardizat Natl Qual Supervis & Testing Ctr RFID Prod Jiangs Nanjing Peoples R China

Millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) is a promising technology for next generation wireless communications. The utilisation of traditional full digital precoding techniques for mmWave massive MIMO systems is too costly. Fortunately, the hybrid (analogue/digital) precoding is a better choice. In this study, the authors investigate a near-optimal iterative approximation hybrid precoding algorithm via cost-efficient sub-connected structure for mmWave massive MIMO systems. Based on the minimum mean square error (MSE) criterion, the optimal design of the proposed hybrid precoders is non-convex. The original problem is reformulated as two optimisation sub-problems, where one of the sub-problems is convex and another is non-convex. First, the authors convert the non-convex sub-problem into a convex problem by relaxing the constant modulus constraint from beampattern with interference control method, and eliminating the block diagonal constraint from vector operation with the properties of Kronecker product. Then the two convex sub-problems are solved iteratively. The proposed algorithm can achieve a highly approximate optimal solution, which can be theoretically demonstrated to converge to a Karush-Kuhn-Tucker point of the original problem. Simulation results show that the proposed algorithm via both sub-connected and fully connected structure gets favourable performance in terms of MSE and achievable rate.

关键词： mean square error methods iterative methods MIMO communication precoding millimetre wave communication convex programming concave programming interference suppression approximation theory millimeter wave massive MIMO systems millimeter wave massive multiple-input multiple-output systems traditional full digital precoding techniques mmWave massive MIMO systems constant modulus block diagonal constraints nonconvex problem convex problem near-optimal hybrid precoding cost-efficient sub-connected structure next-generation wireless communications analogue-digital precoding gigabits per second transmitting data rate gigabits per second transmitting data rate near-optimal iterative approximation hybrid precoding algorithm minimum mean square error criterion optimisation sub-problems beampattern interference control method Kronecker product approximate optimal solution Karush-Kuhn-Tucker point achievable rate MSE

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Solution of security constrained optimal power flow for large-scale power systems by convex transformation techniques and Taylor series

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IET GENERATION TRANSMISSION & DISTRIBUTION 2016年第4期10卷 889-896页

作者： Attarha, Ahmad Amjady, Nima Semnan Univ Dept Elect Engn Semnan Iran

Security constrained optimal power flow (SCOPF) is a key operation function for today's power systems, extensively used, for example, in the dispatching centres. However, SCOPF is a complex optimisation problem for large practical power systems, mostly due to its highly non-convex nature. This study aims at changing highly non-convex SCOPF problem to a convex one. In this way, SCOPF can be solved with much less computation burden and more optimal solutions can be obtained for it by means of commercial solvers. For this purpose, the non-convex terms of SCOPF model (for instance, the terms associated with the valve loading effects of units and AC network modelling) are first reformulated using Signomial functions based on Taylor series. Then, the Signomial SCOPF formulation becomes convex by means of power transformation techniques. The constructed convex SCOPF formulation can be easily solved to obtain its optimal solution. The proposed solution approach is tested on well-known IEEE 30-bus, 118-bus, 300-bus and the polish 2746-bus test systems and its obtained results are compared with the results of several other SCOPF solution methods and published literature figures.

关键词： valve loading effects large-scale power systems power system security Taylor series nonconvex SCOPF problem Polish 2746-bus test systems security constrained optimal power flow solution dispatching centres Optimisation techniques Power system control IEEE bus test system power transformation techniques AC network modelling concave programming convex programming load flow complex optimisation problem convex transformation techniques Signomial functions

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Statistically robust transceiver design algorithms for relay aided multiple-input multiple-output interference systems

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IET SIGNAL PROCESSING 2018年第1期12卷 51-63页

作者： Singh, Vindheshwari P. Chaturvedi, Ajit K. Indian Inst Technol Kanpur Dept Elect Engn Kanpur Uttar Pradesh India IIT Roorkee Dept Elect & Commun Engn Roorkee Uttar Pradesh India

In this study, the authors consider robust transceiver design for amplify-and-forward relay aided multiple-input multiple-output interference systems assuming direct transmitter-receiver links and imperfect channel state information (CSI). The imperfect CSI of each link consists of the estimated channel and the covariance matrix of the channel estimation error. The authors address two transceiver optimisation problems: one is minimising the sum of averaged mean squared error (MSE) at all the receivers and the other is minimising the maximum averaged MSE among all the receivers, both of which are subject to power constraints at the transmitter and relay nodes. The formulated sum-MSE minimisation and max-MSE minimisation based optimisation problems are non-convex with matrix variables and therefore a globally optimal solution is difficult to obtain. To solve these non-convex optimisation problems, they develop sub-optimal iterative algorithms based on alternating minimisation approach to jointly optimise the precoding matrices at the transmitter and relay nodes and the receiver filter matrices. Simulation results demonstrate the effectiveness of the proposed algorithms and their improved performance against CSI uncertainties at similar computational cost as the existing non-robust designs.

关键词： radio transceivers relay networks (telecommunication) MIMO communication radiofrequency interference amplify and forward communication channel estimation radio links covariance matrices mean square error methods concave programming minimax techniques minimisation iterative methods precoding statistically robust transceiver design algorithms amplify-and-forward relay aided multiple-input multiple-output interference systems direct transmitter-receiver links imperfect channel state information CSI covariance matrix channel estimation error averaged mean squared error minimization power constraints sum-MSE minimisation max-MSE minimisation based optimisation problems nonconvex optimisation problems matrix variables sub-optimal iterative algorithms alternating minimisation approach precoding matrices relay nodes receiver filter matrices

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Optimal power allocation for green cognitive radio: fractional programming approach

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IET COMMUNICATIONS 2013年第12期7卷 1279-1286页

作者： Naeem, Muhammad Illanko, Kandasamy Karmokar, Ashok Anpalagan, Alagan Jaseemuddin, Muhammad Ryerson Univ Dept Elect & Comp Engn Toronto ON Canada

In this study, the problem of determining the power allocation that maximises the energy efficiency of cognitive radio network is investigated as a constrained fractional programming problem. The energy-efficient fractional objective is defined in terms of bits per Joule per Hertz. The proposed constrained fractional programming problem is a non-linear non-convex optimisation problem. The authors first transform the energy-efficient maximisation problem into a parametric optimisation problem and then propose an iterative power allocation algorithm that guarantees e-optimal solution. A proof of convergence is also given for the e-optimal algorithm. The proposed e-optimal algorithm provide a practical solution for power allocation in energy-efficient cognitive radio networks. In simulation results, the effect of different system parameters (interference threshold level, number of primary users and number of secondary users) on the performance of the proposed algorithms are investigated.

关键词： Environmental factors energy-efficient maximisation problem environmental factors Optimisation techniques nonlinear programming Îµ-optimal solution nonlinear nonconvex optimisation problem primary users energy-efficient cognitive radio networks iterative methods optimal power allocation concave programming constrained fractional programming problem secondary users parametric optimisation problem Interpolation and function approximation (numerical analysis) green cognitive radio Radio links and equipment interference threshold level cognitive radio energy-efficient fractional objective iterative power allocation algorithm

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