iPiasco swMATH ID: 13492 Software Authors: Ochs, Peter; Brox, Thomas; Pock, Thomas Description: iPiasco: inertial proximal algorithm for strongly convex optimization. In this paper, we present a forward-backward splitting algorithm with additional inertial term for solving a strongly convex optimization problem of a certain type. The strongly convex objective function is assumed to be a sum of a non-smooth convex and a smooth convex function. This additional knowledge is used for deriving a worst-case convergence rate for the proposed algorithm. It is proved to be an optimal algorithm with linear rate of convergence. For certain problems this linear rate of convergence is better than the provably optimal worst-case rate of convergence for smooth strongly convex functions. We demonstrate the efficiency of the proposed algorithm in numerical experiments and examples from image processing. Homepage: http://link.springer.com/article/10.1007%2Fs10851-015-0565-0 Keywords: heavy-ball method; strongly convex optimization; inertial proximal method; convergence analysis Related Software: iPiano; UNLocBoX; AdaGrad; AlexNet; CIFAR; ImageNet; condat_tv; ARock; PDCO; RecPF; RestoVMFB_Lab; ADADELTA; Tunability; MNIST; PyTorch; Adam; BADMM; glasso; APAM; Inertial-SsGM Cited in: 53 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year iPiasco: inertial proximal algorithm for strongly convex optimization. Zbl 1327.90219Ochs, Peter; Brox, Thomas; Pock, Thomas 2015 all top 5 Cited by 91 Authors 17 Shehu, Yekini 6 Dong, Qiaoli 6 Iyiola, Olaniyi Samuel 4 Mewomo, Oluwatosin Temitope 3 Cholamjiak, Prasit 3 Gibali, Aviv 3 Jiang, Dan 3 Ogbuisi, Ferdinard Udochukwu 2 Abubakar, Jamilu 2 Aujol, Jean-François 2 Brox, Thomas 2 Cai, Xingju 2 Chen, Caihua 2 Dang Van Hieu 2 Dương Việt Thông 2 Gao, Xue 2 Izuchukwu, Chinedu 2 Jolaoso, Lateef Olakunle O. 2 Kang, Myeongmin 2 Li, Xiaohuan 2 Ma, Shiqian 2 Ochs, Peter 2 Pock, Thomas 2 Vuong, Phan Tu 2 Yang, Junfeng 1 Alakoya, Timilehin Opeyemi 1 Bednarczuk, Ewa M. 1 Bonettini, Silvia 1 Bruhn, Andrés 1 Cai, Gang 1 Chan, Raymond Hon-Fu 1 Chao, Miantao 1 Chen, Jie 1 Cho, Yeol Je 1 Dosovitskiy, Alexey 1 Dossal, Charles 1 Durou, Jean-Denis 1 Enyi, Cyril Dennis 1 Fan, Jingjing 1 Garba, Isah Abor 1 Grewenig, Sven 1 Guo, Dan Ni 1 Han, Deren 1 Jezierska, Anna 1 Jian, Jinbao 1 Jones, Colin Neil 1 Jung, Miyoun 1 Kang, Myungjoo 1 Ke, Shang-Hong 1 Kesornprom, Suparat 1 Kumam, Poom 1 Labarre, Florian 1 Li, Min 1 Liu, Liya 1 Liu, Pengjie 1 Loizou, Nicolas 1 Maingé, Paul-Emile 1 Peng, Wei 1 Phoha, Shashi P. 1 Prato, Marco 1 Qin, Xiaolong 1 Quéau, Yvain 1 Rassias, Themistocles Michael 1 Ray, Asok 1 Rebegoldi, Simone 1 Rehman, Habib Ur 1 Richtárik, Peter 1 Rondepierre, Aude 1 Rutkowski, Krzysztof E. 1 Saab, Samer jun. 1 Sagratella, Simone 1 Schroers, Christopher 1 Shao, Hu 1 Sidi, Shehu Abubakar 1 Stathopoulos, Giorgos 1 Taiwo, Adeolu 1 Wang, Xiaoquan 1 Wang, Xueye 1 Weickert, Joachim 1 Wu, Ting 1 Wu, Zhongming 1 Xu, Yangyang 1 Xu, Yibo 1 Yan, Yonggui 1 Yao, Jen-Chih 1 Zemkoho, Alain B. 1 Zhang, Hui 1 Zhang, Xiaoya 1 Zhang, Yu Feng 1 Zhong, Lunlong 1 Zhu, Minghui all top 5 Cited in 34 Serials 5 Computational Optimization and Applications 3 Journal of Computational and Applied Mathematics 3 Optimization 3 Journal of Fixed Point Theory and Applications 3 SIAM Journal on Imaging Sciences 2 Calcolo 2 Journal of Optimization Theory and Applications 2 Numerical Functional Analysis and Optimization 2 Journal of Global Optimization 2 Numerical Algorithms 2 Journal of Mathematical Imaging and Vision 2 Optimization Methods & Software 1 Applicable Analysis 1 Commentationes Mathematicae Universitatis Carolinae 1 Results in Mathematics 1 SIAM Journal on Control and Optimization 1 Journal of the Nigerian Mathematical Society 1 Asia-Pacific Journal of Operational Research 1 Journal of Scientific Computing 1 Machine Learning 1 International Journal of Computer Mathematics 1 Mathematical Programming. Series A. Series B 1 SIAM Journal on Optimization 1 International Journal of Computer Vision 1 Computational and Applied Mathematics 1 Mathematical Methods of Operations Research 1 Journal of Inequalities and Applications 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 Thai Journal of Mathematics 1 Fixed Point Theory 1 Networks and Spatial Economics 1 Acta Mathematica Sinica. Chinese Series 1 Set-Valued and Variational Analysis 1 Advances in Pure and Applied Mathematics all top 5 Cited in 13 Fields 33 Operations research, mathematical programming (90-XX) 29 Numerical analysis (65-XX) 27 Operator theory (47-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 7 Computer science (68-XX) 5 Information and communication theory, circuits (94-XX) 2 Partial differential equations (35-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Statistics (62-XX) Citations by Year