Error Analysis of Surrogate Models Constructed Through Operations on Submodels

References

• [1] Audet C, Hare W (2017) Derivative-free and Blackbox Optimization (Springer International Publishing AG, Switzerland).Crossref, Google Scholar
• [2] Audet C, Hare W (2020) Model-based methods in derivative-free nonsmooth optimization. Numerical Nonsmooth Optimization (Springer), 655–691.Crossref, Google Scholar
• [3] Chen Y, Moore KL (2002) Discretization schemes for fractional-order differentiators and integrators. IEEE Trans. Circuits Systems I Fundamental Theory Appl. 49:363–367.Crossref, Google Scholar
• [4] Chen Y, Vinagre BM, Podlubny I (2004) Continued fraction expansion approaches to discretizing fractional order derivatives—An expository review. Nonlinear Dynamics 38:155–170.Crossref, Google Scholar
• [5] Conn A, Scheinberg K, Vicente L (2008) Geometry of interpolation sets in derivative free optimization. Math. Programming 111:141–172.Crossref, Google Scholar
• [6] Conn A, Scheinberg K, Vicente L (2008) Geometry of sample sets in derivative-free optimization: polynomial regression and underdetermined interpolation. IMA J. Numerical Anal. 28:721–748.Crossref, Google Scholar
• [7] Conn A, Scheinberg K, Vicente L (2009) Introduction to Derivative-Free Optimization (SIAM, Philadelphia).Crossref, Google Scholar
• [8] Hare W (2017) Compositions of convex functions and fully linear models. Optim. Lett. 11:1217–1227.Crossref, Google Scholar
• [9] Hare W (2020) A discussion on variational analysis in derivative-free optimization. Set-Valued Variational Anal. 28:643–659.Crossref, Google Scholar
• [10] Hare W, Jarry-Bolduc G (2020) Calculus identities for generalized simplex gradients: Rules and applications. SIAM J. Optim. 30(1):853–884.Crossref, Google Scholar
• [11] Hare W, Nutini J (2013) A derivative-free approximate gradient sampling algorithm for finite minimax problems. Comput. Optim. Appl. 56:1–38.Crossref, Google Scholar
• [12] Hare W, Jarry-Bolduc G, Planiden C (2022) Error bounds for overdetermined and underdetermined generalized centred simplex gradients. IMA J. Numer. Anal. 42(1):744–770.Google Scholar
• [13] Hare W, Jarry-Bolduc G, Planiden C (2020) Hessian approximations. Preprint, submitted November 4, https://arxiv.org/abs/2011.02584.Google Scholar
• [14] Hare W, Planiden C, Sagastizábal C (2020) The chain rule for VU-decompositions of nonsmooth functions. J. Convex Anal. 27(1):335–360.Google Scholar
• [15] Hwang C, Leu JF, Tsay SY (2002) A note on time-domain simulation of feedback fractional-order systems. IEEE Trans. Automatic Control 47(4):625–631.Crossref, Google Scholar
• [16] Kandasamy M, Peri D, Tahara Y, Wilson W, Miozzi M, Georgiev S, Milanov E, Campana EF, Stern F (2013) Simulation based design optimization of waterjet propelled delft catamaran. Internat. Shipbuilding Progress 60(1–4):277–308.Google Scholar
• [17] Khan KA, Larson J, Wild SM (2018) Manifold sampling for optimization of nonconvex functions that are piecewise linear compositions of smooth components. SIAM J. Optim. 28(4):3001–3024.Crossref, Google Scholar
• [18] Larson J, Menickelly M, Wild SM (2016) Manifold sampling for ℓ1 nonconvex optimization. SIAM J. Optim. 26(4):2540–2563.Crossref, Google Scholar
• [19] Larson J, Menickelly M, Zhou B (2021) Manifold sampling for optimizing nonsmooth nonconvex compositions. SIAM J. Optim. 31(4):2638–2664.Google Scholar
• [20] Ling C, Lu Z, Yun W, Zhou S (2021) An efficient method for estimating fuzzy failure probability-based global fuzzy reliability sensitivity. Engrg. Optim. 53(4):576–593.Crossref, Google Scholar
• [21] Maundy B, Elwakil AS, Freeborn TJ (2011) On the practical realization of higher-order filters with fractional stepping. Signal Processing 91(3):484–491.Crossref, Google Scholar
• [22] Rashki M (2018) Hybrid control variates-based simulation method for structural reliability analysis of some problems with low failure probability. Appl. Math. Model. 60:220–234.Crossref, Google Scholar
• [23] Regis R (2015) The calculus of simplex gradients. Optim. Lett. 9:845–865.Crossref, Google Scholar
• [24] Rockafellar RT, Wets RJB (2009) Variational Analysis, vol. 317 (Springer Science & Business Media).Google Scholar
• [25] Wu J-L, Chen C-H (2004) A new operational approach for solving fractional calculus and fractional differential equations numerically. IEICE Trans. Fundamentals Electronics Comm. Comput. Sci. 87(5):1077–1082.Google Scholar
• [26] Zhang X, Pandey MD (2013) Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method. Structural Safety 43:28–40.Crossref, Google Scholar