[1] Alarie, S., Audet, C., Gheribi, A.E., Kokkolaras, M., Le Digabel, S.: Two decades of blackbox optimization applications. EURO J. Comput. Optim. 9, 100011 (2021) [2] Carrillo, J.A., Jin, S., Li, L., Zhu, Y.: A consensus-based global optimization method for high dimensional machine learning problems. ESAIM Control Optim. Calc. Var. 27, S5 (2021) [3] Cartis, C., Roberts, L.: Scalable subspace methods for derivative-free nonlinear least-squares optimization. Math. Program. 199, 461-524 (2023) [4] Chen, L., Stroock, D.W.: The fundamental solution to the Wright-Fisher equation. SIAM J. Math. Anal. 42, 539-567 (2010) [5] Chiang, T.-S., Hwang, C.-R., Sheu, S.J.: Diffusion for global optimization in $\mathbb{R}^n$. SIAM J. Control. Optim. 25(3), 737-753 (1987) [6] Chow, S.-N., Yang, T.-S., Zhou, H.-M.: Global optimizations by intermittent diffusion. In: Chaos, CNN, Memristors and Beyond: a Festschrift for Leon Chua With DVD-ROM, composed by Eleonora Bilotta, pp. 466-479. World Scientific (2013) [7] Conn, A.R., Scheinberg, K., Vicente, L.N.: Introduction to Derivative-free Optimization. SIAM, Philadelphia (2009) [8] Dekkers, A., Aarts, E.: Global optimization and simulated annealing. Math. Program. 50(1), 367-393 (1991) [9] Engquist, B., Ren, K., Yang, Y.: An algebraically converging stochastic gradient descent algorithm for global optimization. arXiv:2204.05923 (2022) [10] Epstein, C.L., Mazzeo, R.: Wright-Fisher diffusion in one dimension. SIAM J. Math. Anal. 42, 568-608 (2010) [11] Fabes, E.B., Kenig, C.E., Serapioni, R.P.: The local regularity of solutions of degenerate elliptic equations. Commun. Stat. Theory Methods 7(1), 77-116 (1982) [12] Fornasier, M., Klock, T., Riedl, K:. Consensus-based optimization methods converge globally. arXiv:2103.15130v4 (2021) [13] Fragnelli, G., Mugnai, D.: Carleman estimates, observability inequalities and null controllability for interior degenerate non smooth parabolic equations. Memoirs of the American Mathematical Society, 242(1146) (2016) [14] Fragnelli, G., Ruiz Goldstein, G., Goldstein, J.A., Romanelli, S.: Generators with interior degeneracy on spaces of l2 type. Electron. J. Differ. Equ. 2012, 1-30 (2012) [15] Frederick, C., Egerstedt, M., Zhou, H.: Collective motion planning for a group of robots using intermittent diffusion. J. Sci. Comput. 90(1), 1-20 (2022) [16] Gelfand, S.B., Mitter, S.K.: Recursive stochastic algorithms for global optimization in $\mathbb{R}^d$. SIAM J. Control. Optim. 29, 999-1018 (1991) [17] Geman, S., Hwang, C.-R.: Diffusions for global optimization. SIAM J. Control. Optim. 24, 1031-1043 (1986) [18] Haupt, R.L., Haupt, S.E.: Practical Genetic Algorithms. Wiley, New York (2004) [19] Heinonen, J., Kipelainen, T., Martio, O.: Nonlinear Potential Theory of Degenerate Elliptic Equations. Courier Dover Publications, Mineola (2018) [20] Henderson, D., Jacobson, S.H., Johnson, A.W.: The theory and practice of simulated annealing. In: Handbook of Metaheuristics, pp. 287-319. Springer (2003) [21] Holland, J.H.: Holland. Genetic algorithms. Sci. Am. 267, 66-73 (1992) [22] Kirkpatrick, S., Daniel Gelatt, C., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671-680 (1983) [23] Kolda, T.G., Lewis, R.M., Torczon, V.: Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev. 45, 385-482 (2003) [24] Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E.: Convergence properties of the Nelder-Mead simplex method in low dimensions. SIAM J. Optim. 9, 112-147 (1998) [25] Larson, J., Menickelly, M., Wild, S.M.: Derivative-free optimization methods. Acta Numer. 28, 287-404 (2019) [26] McKinnon, K.I.M.: Convergence of the Nelder-Mead simplex method to a non-stationary point. SIAM J. Optim. 9, 148-158 (1999) [27] Mitchell, M.: An Introduction to Genetic Algorithms. MIT Press, Cambridge (1998) [28] Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7, 308-313 (1965) [29] Oleınik, O.A.: Linear equations of second order with nonnegative characteristic form. Mat. Sb. (NS) 69, 111-140 (1966) [30] Pérez, C., Rela, E.: Degenerate Poincaré-Sobolev inequalities. Trans. Am. Math. Soc. 372(9), 6087-6133 (2019) [31] Poli, R., Kennedy, J., Blackwell, T.: Particle swarm optimization. Swarm Intell. 1, 33-57 (2007) [32] Rastrigin, L.A.: Systems of Extremal Control. Nauka, Moscow (1974) [33] Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: 1998 IEEE International Conference on Evolutionary Computation Proceedings, pp. 69-73 (1998) [34] Stroock, D.W., Srinivasa Varadhan, S.R.: Multidimensional Diffusion Processes. Springer Science & Business Media, Berlin (1997) [35] Totzeck, C.: Trends in consensus-based optimization. arXiv:2104.01383 (2021) |