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DIFFERENCE-OF-CONVEX algorithmS FOR A CLASS OF SPARSE GROUP l0 REGULARIZED OPTIMIZATION PROBLEMS

SIAM JOURNAL ON OPTIMIZATION 2022年第3期32卷 1614-1641页

作者： Li, Wenjing Bian, Wei Toh, Kim-Chuan Natl Univ Singapore Dept Math 10 Lower Kent Ridge Rd Singapore Singapore Harbin Inst Technol Sch Math Harbin 150001 Peoples R China Natl Univ Singapore Inst Operat Res & Analyt 10 Lower Kent Ridge Rd Singapore Singapore

In this paper, we consider a class of sparse group l(0) regularized optimization problems. First, we give a continuous relaxation model of the considered problem and define a class of stationary points of the relaxation problem. Then, we establish the equivalence of these two problems in the sense of global minimizers, and prove that the defined stationary point is equivalent to the local minimizer of the considered sparse group l(0) regularized problem with a desirable bound from its global minimizers. Further, based on the difference-of-convex (dc) structure of the relaxation problem, we design two dc algorithms to solve the relaxation problem. We prove that any accumulation point of the iterates generated by them is a local minimizer with a desirable bound for the considered sparse group l(0) problem. In particular, all accumulation points have a common support set and their zero entries can be attained within finite iterations. Moreover, we give the global convergence analysis of the proposed algorithms. Finally, we perform some numerical experiments to show the efficiency of the proposed algorithms.

关键词： sparse group l(0) regularization continuous relaxation dc algorithm global convergence

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Behavior of dcA sequences for solving the trust-region subproblem

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JOURNAL OF GLOBAL OPTIMIZATION 2012年第2期53卷 317-329页

作者： Hoai An Le Thi Tao Pham Dinh Nguyen Dong Yen Paul Verlaine Univ Metz Lab Theoret & Appl Comp Sci LITA F-57045 Metz France Natl Inst Appl Sci INSA Rouen Lab Modelling Optimizat & Operat Res LMI F-76801 St Etienne France Vietnamese Acad Sci & Technol Inst Math Hanoi 10307 Vietnam

From our results it follows that any dcA sequence for solving the trust-region subproblem (see Pham Dinh and Le Thi, in SIAM J Optim 8:476-505, 1998) is convergent provided that the basic matrix of the problem is nonsingular and it does not have multiple negative eigenvalues. Besides, under this additional assumption, there exists such an open set containing the global minimizers and the unique local-nonglobal minimizer (if such exists) that any dcA sequence with the initial point from is contained in the set and converges to a global minimizer or the local-nonglobal minimizer. Various examples are given to illustrate the limiting behavior and stability of the dcA sequences. Structure of the KKT point set of the trust-region subproblem is also analyzed.

关键词： Trust-region subproblem dc algorithm dcA sequence Limiting behavior and stability Multiplicity of nonpositive eigenvalue

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An Interval-Reduced-Basis Approach for Predicting Acoustic Response of Coupled Structural-Acoustic System 5th

An Interval-Reduced-Basis Approach for Predicting Acoustic R...

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5th International Conference on Electrical Engineering and Automatic Control (ICEEAC)

作者： Lv, Zheng Qiu, Zhiping Li, Qi Beihang Univ Sch Aeronaut Sci & Engn Beijing 100191 Peoples R China

ISBN: (纸本)9783662487686;9783662487662

To predict and improve the acoustic behavior, an interval-reduced-basis approach is presented for acoustic response of coupled structural-acoustic system. In the present approach, the acoustic response is approximated by using a linear combination of interval-basis vectors with undetermined coefficients. The reduced-order equations are derived based on Galerkin scheme to compute the undetermined coefficients. In addition, the determination of the acoustic response range is transformed into a sequence of quadratic programming problems subject to box constraints, which are computed using the dc algorithm effectively. Numerical example is presented to demonstrate the implementation of the present approach and show that the new approach has a good accuracy and efficiency.

关键词： Interval-reduced-basis approach Acoustic response Coupled structural-acoustic system Quadratic programming problem dc algorithm

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Behavior of dcA sequences for solving the trust-region subproblem

Behavior of DCA sequences for solving the trust-region subpr...

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International Conference on Optimization and its Applications (ICOIA)

关键词： Trust-region subproblem dc algorithm dcA sequence Limiting behavior and stability Multiplicity of nonpositive eigenvalue

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A New Approach for Optimizing Traffic Signals in Networks Considering Rerouting 3rd

A New Approach for Optimizing Traffic Signals in Networks Co...

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3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO)

作者： Duc Quynh Tran Ba Thang Phan Nguyen Quang Thuan Nguyen Vietnam Natl Univ Agr FITA Hanoi Vietnam Hanoi Univ Sci & Technol SAMI Hanoi Vietnam

ISBN: (纸本)9783319181615;9783319181608

In traffic signal control, the determination of the green time and the cycle time for optimizing the total delay time is an important problem. We investigate the problem by considering the change of the associated flows at User Equilibrium resulting from the given signal timings (rerouting). Existing models are solved by the heuristic-based solution methods that require commercial simulation softwares. In this work, we build two new formulations for the problem above and propose two methods to directly solve them. These are based on genetic algorithms (GA) and difference of convex functions algorithms (dcA).

关键词： dc algorithm Genetic algorithm Traffic signal control Bi-level optimization model

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A New Solution Method for a Mean-Risk Mixed Integer Nonlinear Program in Transportation Network Protection 6th

A New Solution Method for a Mean-Risk Mixed Integer Nonlinea...

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6th International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA)

作者： Luong Vuong Le Quang Thuan Nguyen Duc Quynh Tran Hanoi Univ Sci & Technol Hanoi Vietnam Ind Univ Ho Chi Minh City Ho Chi Minh City Vietnam Vietnam Natl Univ Hanoi Int Sch Hanoi Vietnam

ISBN: (纸本)9783030383640;9783030383633

The paper deals with a transportation network protection problem. The aim is to limit losses due to disasters by choosing an optimal retrofiting plan. The mathematical model given by Lu, Gupte, Huang [11] is a mixed integer non linear optimization problem. Existing solution methods are complicated and their computing time is long. Hence, it is necessary to develop efficient solution methods for the considered model. Our approach is based on dc (difference of two convex functions) programming and dc algorithm (dcA). The original model is first reformulated as a dc program by using exact penalty techniques. We then apply dcA to solve the resulting problem. Numerical results on a small network are reported to see the behavior of dcA. It shows that dcA is fast and the proposed approach is promissing.

关键词： dc programming dc algorithm Penalty function Transportation Retrofitting CVaR

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Multi-UAV trajectory planning problem using the difference of convex function programming 62

Multi-UAV trajectory planning problem using the difference o...

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62nd IEEE Conference on Decision and Control (Cdc)

作者： Anh Phuong Ngo Thomas, Christan Karimoddini, Ali Nguyen, Hieu T. North Carolina A&T State Univ Dept Elect & Comp Engn Greensboro NC 27411 USA Lockheed Martin Corp Dept Flight Test Ft Worth TX 76108 USA

ISBN: (纸本)9798350301243

Trajectory planning for a swarm of UAVs is known as a challenging nonconvex optimization problem, particularly due to a large number of collision avoidance constraints required for individual pairs of UAVs in the swarm. In this paper, we tackle this nonconvexity by leveraging the difference of convex function (dc) programming. We introduce the slack variables to relax and reformulate the collision avoidance conditions and employ the penalty function term to equivalently convert the problem into the dc form. Consequently, we construct a penalty dc algorithm in which we sequentially solve a set of convex optimization problems obtained by linearizing the collision avoidance constraint. The algorithm iteratively tightens the safety condition and reduces the objective cost of the planning problem and the additional penalty term. Numerical results demonstrate the effectiveness of the proposed approach in planning a large number of UAVs in congested space.

关键词： Trajectory planning dc programming penalty dc algorithm collision avoidance non-convex optimization

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Solving Relaxation Orienteering Problem Using dcA-CUT 3rd

Solving Relaxation Orienteering Problem Using DCA-CUT

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3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO)

作者： Anh Son Ta Hoai An Le Thi Trong Sy Ha Hanoi Univ Sicence & Technol SAMI Hanoi Vietnam Lorraine Univ LITA Metz France

ISBN: (纸本)9783319181615;9783319181608

Orienteering problem is well-known as a NP-hard problem in transportation with many applications. This problem aims to find a path between a given set of control points, where the source and destination points are specified with respect to maximize the total score of collected points and satisfy the distance constraint. In this paper, we first analyze the structure of a generalized orienting problem and a new solution method, based on dc programming, dcA and Cutting plane method, is introduced. Preliminary numerical experiments are reported to show the efficiency of the proposed algorithm.

关键词： Orienteering problem dc programming dc algorithm Binary Linear Integer Program

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A Novel Approach for Travel Time Optimization in Single-Track Railway Networks 6th

A Novel Approach for Travel Time Optimization in Single-Trac...

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6th International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA)

作者： Nguyen Quang Thuan Nguyen Duc Anh Vietnam Natl Univ Hanoi Int Sch Hanoi Vietnam Hanoi Univ Sci & Technol Hanoi Vietnam

ISBN: (纸本)9783030383640;9783030383633

Train scheduling plays an important role in the operation of railways systems. This work focuses on a model of scheduling in which one minimizes the total travel time of trains in a single track railways network. The model can be written in the form of a mixed 0-1 linear program which has the worst case exponential complexity to calculate the optimal solution. In this paper, we propose a computationally efficient approach to solve the train scheduling problem. Our approach is based on a so-called Difference of Convex functions algorithm (dcA) to provide good feasible solutions with finite convergence. The algorithm is tested on three different railway network topologies including one topology introduced in [18] and two practical topologies in Northern Vietnam. The numerical results are encouraging and demonstrate the efficiency of the approach.

关键词： Train scheduling Penalty function dc algorithm

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Image denoising with a non-monotone boosted dcA for non-convex models

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COMPUTERS & ELECTRICAL ENGINEERING 2024年 117卷

作者： Ferreira, O. P. Rabelo, R. A. L. Ribeiro, P. H. A. Santos, E. M. Souza, J. C. O. Univ Fed Goias IME Goiania Go Brazil Fed Univ Piaui UFPI Elect Engn Teresina PI Brazil Fed Inst Educ Sci & Technol Maranhao Sci & Technol Maranhao Pinheiro MA Brazil Fed Inst Educ Sci & Technol Maranhao Barra Corda MA Brazil Univ Fed Piaui Dept Math Teresina PI Brazil

Image reconstruction is important for activities that rely on optical and comparative data analysis. Signals obtained through acquisition systems can be inconsistent due to several factors, such as camera movement and noise, but they can be modeled mathematically. With this, continuous optimization tools have become popular in recent years for image problems. This work seeks to reconstruct noisy images using a non -monotone boosted dc algorithm (nmBdcA), an accelerated variant of the Difference of Convex algorithm (dcA), with a non-convex version of the total variation (TV) model, to obtain better computational performance than dcA and superior quality of the restored image. Specifically, the performance of the non-convex TV model is compared to its convex formulation. Two sections of experiments are included, one with black-and-white images and another with grayscale medical computed tomography (CT) images. The results of the first section emphasize that nmBdcA performs reconstructions with higher PSNR in all experiments, lower CPU time, and SSIM greater or equal to dcA in 91.67% of tests. The non-convex TV model is more robust than the convex one in the presence of more noise, presenting higher SSIM and PSNR in all experiments performed. In the section of experiments with CT images, nmBdcA outperforms dcA in reconstruction quality and CPU time in all tests performed. The performance of the non-convex model applied with nmBdcA outperforms the convex model in SSIM and CPU time in all experiments, being superior in PSNR in 77.78% of the tests.

关键词： Image denoising Total variation Non-convex optimization dc function dc algorithm

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