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Publications

Journal Publications

Continuous Optimization

  1. Sabach, S. and Teboulle, M. Faster Lagrangian-based methods in convex optimization, accepted for publication in SIAM Journal on Optimization. preprint
  2. Gur, E., Sabach, S. and Shtern, S. Convergent nested alternating minimization algorithms for non-convex optimization problems, accepted for publication in Mathematics of Operations Research. preprint
  3. Cohen, E., Sabach, S. and Teboulle, M. Non-Euclidean proximal methods for convex-concave saddle-point problems, Journal of Applied and Numerical Optimization 3 (2021), 43–60. preprint
  4. Gur, E., Sabach, S. and Shtern, S. Alternating minimization based first-order method for the wireless sensor network localization problem, IEEE Transactions on Signal Processing 68 (2020), 6418–6431. preprint
  5. Gibali, A., Sabach, S. and Voldman, S.: Non-convex split feasibility problems: models, algorithms and theory,  Open Journal of Mathematical Optimization 1 (2020), 1–15. preprint
  6. Chandra, M., Ochs, P., Pock, T. and Sabach, S. Convex-concave backtracking for inertial Bregman proximal gradient algorithms in non-convex optimization, SIAM Journal on Mathematics of Data Sciences 2 (2020), 658–682. preprint
  7. Hazan, T., Sabach, S., and Voldman, S. Stochastic proximal linear method for structured non-convex problems, Optimization Methods and Software 35 (2020), 921–937. preprint
  8. Garber, D., Kaplan, A., and Sabach, S. Improved complexities of conditional gradient-type methods with applications to robust matrix recovery problems, Mathematical Programming (Ser A.) 186 (2019), 185–208. preprint
  9. Luke, D. R., Sabach, S., and Teboulle, M. Optimization on spheres: models and proximal algorithms with computational performance comparison, SIAM Journal on Mathematics of Data Sciences 1 (2019), 408–445. preprint
  10. Sabach, S. and Teboulle, M. Lagrangian methods for composite optimization, Handbook of Numerical Analysis 20 (2019), 401–436. preprint
  11. Sabach, S., Teboulle, M. and Voldman, S. A smoothing alternating minimization-based algorithm for clustering with sum-min of Euclidean norms, Pure and Applied Functional Analysis 3 (2018), 653–679. preprint
  12. Bolte, J., Sabach, S., Teboulle, M. and Vaisbourd, Y. First order methods beyond convexity and Lipschitz gradient continuity with applications to quadratic inverse problems, SIAM Journal on Optimization 28 (2018), 2131–2151. preprint
  13. Bolte, J., Sabach, S. and Teboulle, M. Nonconvex Lagrangian-based optimization: monitoring schemes and global convergence, Mathematics of Operations Research 43 (2018), 1210–1232. preprint
  14. Beck, A., Eldar, Y. C., Pauwels, E. and Sabach, S. On Fienup methods for regularized phase retrieval, IEEE Transactions on Signal Processing 66 (2018), 982–991. preprint
  15. Luke, D. R., Sabach, S., Teboulle, M., and Zatlawey, K. A simple globally convergent algorithm for the single source localization problem, Journal of Global Optimization 69 (2017), 889–909. preprint
  16. Sabach, S. and Shtern, S. A first order method for solving convex bi-level optimization problems. SIAM Journal on Optimization 27 (2017), 640–660. preprint
  17. Beck, A., Pauwels, E. and Sabach, S. Primal and dual predicted decrease approximation methods, Mathematical Programming (Ser B.) 167 (2018), 37–73. preprint
  18. Pock, T. and Sabach, S. Inertial proximal alternating linearized minimization (iPALM) for nonconvex and nonsmooth problems, SIAM Journal on Imaging Sciences 9 (2016), 1756–1787. preprint
  19. Beck, A., Sabach, S. and Teboulle, M. An alternating semiproximal method for nonconvex regularized structured total least squares problems, SIAM. J. Matrix Anal. & Appl. 37 (2016), 1129–1150. preprint
  20. Beck, A., Pauwels, E. and Sabach, S. The cyclic block conditional gradient method for convex optimization problems, SIAM Journal on Optimization 25 (2015), 2024–2049. preprint
  21. Hesse, R., Luke, D. R., Sabach, S. and Tam, M. K. Proximal heterogeneous block implicit explicit method and application to blind ptychographic diffraction imaging, SIAM Journal on Imaging Sciences 8 (2015), 426–457. preprint
  22. Drori, Y. Sabach, S. and Teboulle, M. A simple algorithm for a class of nonsmooth convex-concave saddle-point problems, Operations Research Letters 43 (2015), 209–214. preprint
  23. Beck, A. and Sabach, S. Weiszfeld’s method: old and new results, Journal of Optimization Theory and Applications 164 (2015), 1–40. preprint
  24. Beck, A. and Sabach, S. A first order method for finding minimal norm-like solutions of convex optimization problems, Mathematical Programming (Ser. A) 147 (2014), 25–46. preprint
  25. Bolte, J., Sabach, S. and Teboulle, M. Proximal alternating linearized minimization for nonconvex and nosmooth problems, Mathematical Programming (Ser. A) 146 (2014), 459–494. preprint
  26. Beck, A. and Sabach, S. An improved ellipsoid method for solving convex differentiable optimization problems, Operations Research Letters 40 (2012), 541–545. preprint
  27. Burachik, R. S., Kaya, C. Y. and Sabach, S. A generalized univariate Newton method motivated by proximal regularization, Journal of Optimization Theory and Applications 155 (2012), 923–940. preprint

Fixed Point Theory

  1. Martin-Marquez, V. Reich, S. and Sabach, S. Bregman strongly nonexpansive operators in reflexive Banach spaces, Journal of Mathematical Analysis and Applications 400 (2013), 597–614. preprint
  2. Martin-Marquez, V., Reich, S. and Sabach, S. Right Bregman nonexpansive operators in Banach spaces, Nonlinear Analysis 75 (2012), 5448–5465. preprint
  3. Borwein, J. M. Reich, S., and Sabach, S. Characterization of Bregman firmly nonexpansive operators using new type of monotonicity, Journal of Nonlinear and Convex Analysis 12 (2011), 161–183. preprint

Optimization in Infinite Dimensional Spaces

  1. Martin-Marquez, V. Reich, S. and Sabach, S. Iterative methods for approximating fixed points of Bregman nonexpansive operators, Discrete and Continuous Dynamical Systems 6 (2013), 1043–1063. preprint
  2. Censor, Y. Gibali, A. Reich S. and Sabach, S. The common variational inequality point problem, Set-Valued and Variational Analysis 20 (2012), 229–247. preprint
  3. Sabach, S. Products of finitely many resolvents of maximal monotone mappings in reflexive Banach spaces, SIAM Journal on Optimization 21 (2011), 1289–1308. preprint
  4. Kassay, G. Reich, S., and Sabach, S. Iterative methods for solving systems of variational inequalities in reflexive Banach spaces, SIAM Journal on Optimization 21 (2011), 1319–1344. preprint
  5. Reich, S. and Sabach, S. A shrinking projection method for Bregman firmly nonexpansive operators in reflexive Banach spaces, Journal of Fixed Point Theory and Applications 9 (2011), 101–116. preprint
  6. Reich, S. and Sabach, S. Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach Spaces, Nonlinear Analysis 73 (2010), 122–135. preprint
  7. Butnariu, D. Reich, S. and Sabach, S. A strong convergence theorem for resolvents of monotone operators, Journal of Convex Analysis 17 (2010), 991–1006. preprint
  8. Reich, S. and Sabach, S. Two strong convergence theorems for a proximal method in reflexive Banach spaces, Numerical Functional Analysis and Optimization 31 (2010), 22–44. preprint
  9. Reich, S. and Sabach, S. A strong convergence theorem for a proximal-type algorithm in reflexive Banach spaces, Journal of Nonlinear and Convex Analysis 10 (2009), 471–485. preprint

Proceedings Publications

  1.  Martin-Marquez, V.Reich, S. and Sabach, S. Existence and approximation of fixed points of right Bregman nonexpansive operators, in Computational and Analytical Mathematics”, Springer, New York, 2012, 501–520. preprint
  2. Reich, S. and Sabach, S. Three strong convergence theorems for iterative methods for solving equilibrium problems in reflexive Banach spaces, in Optimisation Theory and Related Topics”, Contemporary Mathematics, vol. 568, Amer. Math. Soc., Providence, RI, 2012, 225–240. preprint
  3. Reich, S. and Sabach, S. Existence and approximation of fixed points of Bregman firmly nonexpansive mappings in reflexive Banach spaces, in Fixed-Point Algorithms for Inverse Problems in Science and Engineering”, Springer, New York, 2010, 299–314. preprint
  4. Butnariu, D. Resmerita, E. and Sabach, S. A Mosco stability theorem for generalized proximal mappings, in Nonlinear Analysis and Optimization I”, Contemporary Mathematics, vol. 513, Amer. Math. Soc., Providence, RI, 2010, 99–110. preprint

Dissertation

Sabach, S. Iterative Methods for Solving Optimization Problems, Ph.D. dissertation, Department of Mathematics, The Technion, 2012.