An Algorithm for Maximizing a Convex Function Based on Its Minimum

References

• Andrianova A, Korepanova A, Halilova I (2016) One algorithm for branch and bound method for solving concave optimization problem. IOP Conf. Series Material Sci. Engrg. 158:012005.Crossref, Google Scholar
• Audet C, Hansen P, Savard G (2005) Essays and Surveys in Global Optimization, vol. 7 (Springer Science & Business Media, New York).Crossref, Google Scholar
• Beck A (2017) First-Order Methods in Optimization, vol. 25 (SIAM, Philadelphia).Crossref, Google Scholar
• Ben-Israel A, Ben-Tal A, Zlobec S (1981) Optimality in Nonlinear Programming: A Feasible Directions Approach (Wiley, New York).Google Scholar
• Ben-Tal A, Den Hertog D (2014) Hidden conic quadratic representation of some nonconvex quadratic optimization problems. Math. Programming 143(1-2):1–29.Crossref, Google Scholar
• Ben-Tal A, Roos E (2022) Version v2022.0034. Accessed July 22, https://zenodo.org/record/6884872.Google Scholar
• Ben-Tal A, Teboulle M (1996) Hidden convexity in some nonconvex quadratically constrained quadratic programming. Math. Programming 72(1):51–63.Crossref, Google Scholar
• Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Bertsekas DP (1999) Nonlinear Programming, 2nd ed. (Athena Scientific, Nashua, NH).Google Scholar
• Boyd S, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Byrd RH, Nocedal J, Waltz RA (2006) Knitro: An integrated package for nonlinear optimization. Di Pillo G, Roma M, eds. Large-Scale Nonlinear Optimization (Springer US, Boston), 35–59.Crossref, Google Scholar
• Enhbat R (1996) An algorithm for maximizing a convex function over a simple set. J. Global Optim. 8(4):379–391.Crossref, Google Scholar
• Gal S, Bachelis B, Ben-Tal A (1978) On finding the maximal range of validity of a constrained system. SIAM J. Control Optim. 16(3):473–503.Crossref, Google Scholar
• Grippo L, Sciandrone M (2000) On the convergence of the block nonlinear Gauss–Seidel method under convex constraints. Oper. Res. Lett. 26(3):127–136.Crossref, Google Scholar
• Jarre F (1994) Optimal ellipsoidal approximations around the analytic center. Appl. Math. Optim. 30(1):15–19.Crossref, Google Scholar
• Lacoste-Julien S (2016) Convergence rate of Frank-Wolfe for non-convex objectives. Preprint, submitted July 1, https://arxiv.org/abs/1607.00345.Google Scholar
• Le Thi HA, Dinh TP (2018) DC programming and DCA: Thirty years of developments. Math. Programming 169(1):5–68.Crossref, Google Scholar
• Lipp T, Boyd S (2016) Variations and extension of the convex–concave procedure. Optim. Engrg. 17(2):263–287.Crossref, Google Scholar
• Lofberg J (2004) Yalmip: A toolbox for modeling and optimization in Matlab. Proc. IEEE Internat. Conf. on Robotics and Automation (IEEE, New York), 284–289.Crossref, Google Scholar
• Luss R, Teboulle M (2013) Conditional gradient algorithms for rank-one matrix approximations with a sparsity constraint. SIAM Rev. 55(1):65–98.Crossref, Google Scholar
• Mangasarian O (1996) Machine learning via polyhedral concave minimization. Applied Mathematics and Parallel Computing (Springer, Berlin), 175–188.Crossref, Google Scholar
• MOSEK ApS (2020) The MOSEK Optimization Toolbox for MATLAB manual. Version 9.2.35. Accessed July 10, 2021, https://docs.mosek.com/9.2/toolbox/index.html.Google Scholar
• Pardalos PM, Rosen JB (1986) Methods for global concave minimization: A bibliographic survey. SIAM Rev. 28(3):367–379.Crossref, Google Scholar
• Selvi A, Ben-Tal A, Brekelmans R, Den Hertog D (2022) Convex maximization via adjustable robust optimization. INFORMS J. Comput., ePub ahead of print February 17, https://doi.org/10.1287/ijoc.2021.1134.Google Scholar
• Tawarmalani M, Sahinidis NV (2005) A polyhedral branch-and-cut approach to global optimization. Math. Programming 103:225–249.Crossref, Google Scholar
• Zass R, Shashua A (2007) Nonnegative sparse PCA, vol. 19. Schölkopf B, Platt JC, Hoffman T, eds. Advances in Neural Information Processing Systems (MIT Press, Cambridge, MA), 1561–1568.Crossref, Google Scholar
• Zwart PB (1974) Global maximization of a convex function with linear inequality constraints. Oper. Res. 22(3):602–609.Link, Google Scholar