An Adaptive Forward-Backward-Forward Splitting Algorithm for Solving Pseudo-Monotone Inclusions

References

• [1] Adly S, Bourdin L, Caubet F (2019) On a decomposition formula for the proximal operator of the sum of two convex functions. J. Convex Anal. 26(3):699–718.Google Scholar
• [2] Aholt C, Agarwal S, Thomas R (2012) A QCQP approach to triangulation. Fitzgibbon A, Lazebnik S, Perona P, Sato Y, Schmid C, eds. Computer Vision (Springer, Berlin, Heidelberg), 654–667.Google Scholar
• [3] Alacaoglu A, Kim D, Wright SJ (2024) Extending the reach of first-order algorithms for nonconvex min-max problems with cohypomonotonicity. Preprint, submitted February 7, https://arxiv.org/abs/2402.05071.Google Scholar
• [4] Aussel D (1998) Subdifferential properties of quasiconvex and pseudoconvex functions: Unified approach. J. Optim. Theory Appl. 97(1):29–45.Crossref, Google Scholar
• [5] Bauschke H, Combettes P (2017) Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2nd ed. (Springer, Cham, Switzerland).Crossref, Google Scholar
• [6] Borwein JM, Lewis AS (2006) Convex Analysis and Nonlinear Optimization: Theory and Examples (Springer Science and Business Media, New York).Crossref, Google Scholar
• [7] Bot RI, Csetnek ER, Vuong PT (2020) The forward-backward-forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces. Eur. J. Oper. Res. 287(1):49–60.Crossref, Google Scholar
• [8] Briceno-Arias LM, Davis D (2018) Forward-backward-half forward algorithm for solving monotone inclusions. SIAM J. Optim. 28(4):2839–2871.Crossref, Google Scholar
• [9] Browder FE (1967) Convergence theorems for sequences of nonlinear operators in Banach spaces. Mathematische Zeitschrift 100:201–225.Crossref, Google Scholar
• [10] Bùi MN, Combettes PL (2022) Multivariate monotone inclusions in saddle form. Math. Oper. Res. 47(2):1082–1109.Link, Google Scholar
• [11] Cai Y, Zheng W (2022) Accelerated single-call methods for constrained min-max optimization. Internat. Conf. Learn. Representations.Google Scholar
• [12] Cambini A, Crouzeix J-P, Martein L (2002) On the pseudoconvexity of a quadratic fractional function. Optimization 51(4):677–687.Crossref, Google Scholar
• [13] Carosi L, Martein L (2007) On the pseudoconvexity and pseudolinearity of some classes of fractional functions. Optimization 56(3):385–398.Crossref, Google Scholar
• [14] Chambolle A, Pock T (2011) A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vision 40:120–145.Crossref, Google Scholar
• [15] Chen R, Liu AL (2021) A distributed algorithm for high-dimension convex quadratically constrained quadratic programs. Comput. Optim. Appl. 80:781–830.Crossref, Google Scholar
• [16] Chorobura F, Necoara I (2023) Random coordinate descent methods for nonseparable composite optimization. SIAM J. Optim. 33(3):2160–2190.Crossref, Google Scholar
• [17] Combettes PL (2024) The geometry of monotone operator splitting methods. Acta Numerica 33:487–632.Crossref, Google Scholar
• [18] Combettes PL, Pesquet J-C (2012) Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators. Set-Valued Variational Anal. 20:307–330.Crossref, Google Scholar
• [19] Condat L (2013) A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms. J. Optim. Theory Appl. 158:460–479.Crossref, Google Scholar
• [20] Davis D, Yin W (2017) A three-operator splitting scheme and its optimization applications. Set-Valued Variational Anal. 25(4):829–858.Crossref, Google Scholar
• [21] De Maio A, Huang Y, Palomar D, Zhang S, Farina A (2011) Fractional QCQP with applications in ML steering direction estimation for radar detection. IEEE Trans. Signal Processing 59(1):172–185.Crossref, Google Scholar
• [22] Diakonikolas J, Daskalakis C, Jordan M (2021) Efficient methods for structured nonconvex-nonconcave min-max optimization. Proc. 24th Internat. Conf. Artificial Intelligence Statist. (AISTATS) 2021, vol. 130 (PMLR, New York), 2746–2754.Google Scholar
• [23] Gurobi (2025) Gurobi optimizer reference manual. https://www.gurobi.com.Google Scholar
• [24] Hassouni A, Jaddar A (2007) On pseudoconvex functions and applications to global optimization. ESAIM Proc., vol. 20, 138–148.Crossref, Google Scholar
• [25] Hinder O, Sidford A, Sohoni N (2020) Near-optimal methods for minimizing star-convex functions and beyond. Abernethy J, Agarwal S, eds. Proc. Thirty Third Conf. Learn. Theory, vol. 125 (PMLR, New York), 1894–1938.Google Scholar
• [26] Huang Y, Palomar DP (2014) Randomized algorithms for optimal solutions of double-sided QCQP with applications in signal processing. IEEE Trans. Signal Processing 62(5):1093–1108.Crossref, Google Scholar
• [27] Jiang X, Vandenberghe L (2023) Bregman three-operator splitting methods. J. Optim. Theory Appl. 196:936–972.Crossref, Google Scholar
• [28] Karamardian S, Schaible S (1990) Seven kinds of monotone maps. J. Optim. Theory Appl. 66:37–46.Crossref, Google Scholar
• [29] Lanckriet GR, Cristianini N, Bartlett PL, Ghaoui LE, Jordan M (2004) Learning the kernel matrix with semi-definite programming. J. Machine Learn. Res. 5:27–72.Google Scholar
• [30] Latafat P, Themelis A, Stella L, Patrinos P (2024) Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient. Math. Programming 213:433–471.Crossref, Google Scholar
• [31] Malitsky Y (2020) Golden ratio algorithms for variational inequalities. Math. Programming 184:383–410.Crossref, Google Scholar
• [32] Mangasarian OL (1965) Pseudo-convex functions. SIAM J. Control Optim. 3(2):281–290.Google Scholar
• [33] Martein L, Carosi L (2012) The sum of a linear and a linear fractional function: Pseudoconvexity on the nonnegative orthant and solution methods. Bull. Malaysian Math. Sci. 35(2A):591–599.Google Scholar
• [34] Necoara I, Chorobura F (2024) Efficiency of stochastic coordinate proximal gradient methods on nonseparable composite optimization. Math. Oper. Res. 50(2):993–1018.Google Scholar
• [35] Nemirovski A (2004) Prox-method with rate of convergence O(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM J. Optim. 15(1):229–251.Crossref, Google Scholar
• [36] Nesterov Y (2015) Universal gradient methods for convex optimization problems. Math. Programming 152(1–2):381–404.Crossref, Google Scholar
• [37] Panayotis M, Papadimitriou C, Piliouras G (2018) Cycles in adversarial regularized learning. ACM-SIAM Sympos. Discrete Algorithms, 2703–2717.Google Scholar
• [38] Pethick T, Latafat P, Patrinos P, Fercoq O, Cevher V (2022) Escaping limit cycles: Global convergence for constrained nonconvex-nonconcave minimax problems. Internat. Conf. Learn. Representations.Google Scholar
• [39] Schaible S (1981) Quasiconvex, pseudoconvex, and strictly pseudoconvex quadratic functions. J. Optim. Theory Appl. 35(3):303–338.Crossref, Google Scholar
• [40] Thong DV, Vuong PT (2019) Modified Tseng’s extragradient methods for solving pseudo-monotone variational inequalities. Optimization 68(11):2207–2226.Crossref, Google Scholar
• [41] Tongnoi B (2024) A modified Tseng’s algorithm with extrapolation from the past for pseudo-monotone variational inequalities. Taiwanese J. Math. 28(1):187–210.Crossref, Google Scholar
• [42] Tseng P (2000) A modified forward-backward splitting method for maximal monotone mappings. SIAM J. Control Optim. 38(2):431–446.Crossref, Google Scholar
• [43] Yashtini M (2016) On the global convergence rate of the gradient descent method for functions with Hölder continuous gradients. Optim. Lett. 10(6):1361–1370.Crossref, Google Scholar