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; ARock; PDCO; RecPF; Inertial-SsGM; HOGWILD; GitHub; AdaGrad; CIFAR; AIR tools; AlexNet; Saga; ImageNet; LIBSVM; QVILIB; JuMP; UNLocBoX; Rice Wavelet Toolbox; TwIST; DAFNE Cited in: 47 Publications 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 74 Authors 16 Shehu, Yekini 6 Dong, Qiaoli 6 Iyiola, Olaniyi Samuel 4 Mewomo, Oluwatosin Temitope 3 Cholamjiak, Prasit 3 Gibali, Aviv 3 Jiang, Dan 2 Abubakar, Jamilu 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 2 Kang, Myeongmin 2 Li, Xiaohuan 2 Ma, Shiqian 2 Ochs, Peter 2 Ogbuisi, Ferdinard Udochukwu 2 Pock, Thomas 2 Vuong, Phan Tu 2 Yang, Junfeng 1 Alakoya, Timilehin Opeyemi 1 Aujol, Jean-François 1 Bednarczuk, Ewa M. 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 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 Loizou, Nicolas 1 Maingé, Paul-Emile 1 Qin, Xiaolong 1 Quéau, Yvain 1 Rassias, Themistocles Michael 1 Rehman, Habib Ur 1 Richtárik, Peter 1 Rutkowski, Krzysztof E. 1 Sagratella, Simone 1 Schroers, Christopher 1 Sidi, Shehu Abubakar 1 Stathopoulos, Giorgos 1 Taiwo, Adeolu 1 Wang, Xueye 1 Weickert, Joachim 1 Wu, Zhongming 1 Xu, Yangyang 1 Xu, Yibo 1 Yan, Yonggui 1 Zemkoho, Alain B. 1 Zhang, Yu Feng 1 Zhong, Lunlong all top 5 Cited in 30 Serials 4 Computational Optimization and Applications 3 Optimization 3 Journal of Fixed Point Theory and Applications 3 SIAM Journal on Imaging Sciences 2 Calcolo 2 Journal of Computational and Applied Mathematics 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 International Journal of Computer Mathematics 1 SIAM Journal on Optimization 1 International Journal of Computer Vision 1 Computational and Applied Mathematics 1 Journal of Inequalities and Applications 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 Thai Journal of Mathematics 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 27 Numerical analysis (65-XX) 27 Operations research, mathematical programming (90-XX) 25 Operator theory (47-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 6 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