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February 19, 2019 - May 1, 2026

Available Issues

February 19, 2019 - May 1, 2026

A Stochastic Inexact Sequential Quadratic Optimization Algorithm for Nonlinear Equality-Constrained Optimization

Published Online:24 May 2024https://doi.org/10.1287/ijoo.2022.0008

References

  • Achiam J, Held D, Tamar A, Abbeel P (2017) Constrained policy optimization. Precup D, Teh YW, eds. Proc. 34th Internat. Conf. Machine Learn., vol. 70 (PMLR, New York), 22–31.Google Scholar
  • Berahas AS, Curtis FE, O’Neill MJ, Robinson DP (2023) A stochastic sequential quadratic optimization algorithm for nonlinear-equality-constrained optimization with rank-deficient Jacobians. Math. Oper. Res., ePub ahead of print October 30, https://doi.org/10.1287/moor.2021.0154.Google Scholar
  • Berahas AS, Curtis FE, Robinson DP, Zhou B (2021) Sequential quadratic optimization for nonlinear equality constrained stochastic optimization. SIAM J. Optim. 31(2):1352–1379.Google Scholar
  • Biros G, Ghattas O (2003) Inexactness issues in the Lagrange–Newton–Krylov–Schur method for PDE-constrained optimization. Biegler LT, Ghattas O, Heinkenschloss M, Van Bloemen Waanders B, eds. Large-Scale PDE-Constrained Optimization (Springer, New York), 93–114.Google Scholar
  • Bottou L, Curtis FE, Nocedal J (2018) Optimization methods for large-scale machine learning. SIAM Rev. 60(2):223–311.Google Scholar
  • Byrd RH, Curtis FE, Nocedal J (2008) An inexact SQP method for equality constrained optimization. SIAM J. Optim. 19(1):351–369.Google Scholar
  • Byrd RH, Curtis FE, Nocedal J (2010) An inexact Newton method for nonconvex equality constrained optimization. Math. Programming 122(2):273–299.Google Scholar
  • Chatterjee N, Chen YH, Maas P, Carroll RJ (2016) Constrained maximum likelihood estimation for model calibration using summary-level information from external big data sources. J. Amer. Statist. Assoc. 111(513):107–117.Google Scholar
  • Chen C, Tung F, Vedula N, Mori G (2018) Constraint-aware deep neural network compression. Ferrari V, Hebert M, Sminchisescu C, Weiss Y, eds. Computer Vision – ECCV 2018. ECCV 2018 (Springer, Berlin, Heidelberg), 409–424.Google Scholar
  • Choi SCT, Paige CC, Saunders MA (2011) MINRES-QLP: A Krylov subspace method for indefinite or singular symmetric systems. SIAM J. Sci. Comput. 33(4):1810–1836.Google Scholar
  • Courant R (1943) Variational methods for the solution of problems of equilibrium and vibrations. Bull. Amer. Math. Soc. 49(1):1–23.Google Scholar
  • Curtis FE, Nocedal J, Wächter A (2009) A matrix-free algorithm for equality constrained optimization problems with rank-deficient Jacobians. SIAM J. Optim. 20(3):1224–1249.Google Scholar
  • Curtis FE, O’Neill MJ, Robinson DP (2024) Worst-case complexity of an SQP method for nonlinear equality constrained stochastic optimization. Math. Programming 205(1):431–483.Google Scholar
  • Fletcher R (2000) Practical Methods of Optimization (John Wiley & Sons, New York).Google Scholar
  • Geyer CJ (1991) Constrained maximum likelihood exemplified by isotonic convex logistic regression. J. Amer. Statist. Assoc. 86(415):717–724.Google Scholar
  • Gill PE, Murray W, Saunders MA (2002) SNOPT: An SQP algorithm for large-scale constrained optimization. SIAM J. Optim. 12(4):979–1006.Google Scholar
  • Gould NIM, Orban D, Toint PL (2015) CUTEst: A constrained and unconstrained testing environment with safe threads for mathematical optimization. Comput. Optim. Appl. 60:545–557.Google Scholar
  • Han SP (1977) A globally convergent method for nonlinear programming. J. Optim. Theory Appl. 22(3):297–309.Google Scholar
  • Han SP, Mangasarian OL (1979) Exact penalty functions in nonlinear programming. Math. Programming 17(1):251–269.Google Scholar
  • Heinkenschloss M, Ridzal D (2008) An inexact trust-region SQP method with applications to PDE-constrained optimization. Kunisch K, Of G, Steinbach O, eds. Numer. Math. Advanced Appl. (Springer, Berlin, Heidelberg), 613–620.Google Scholar
  • Heinkenschloss M, Vicente LN (2002) Analysis of inexact trust-region SQP algorithms. SIAM J. Optim. 12(2):283–302.Google Scholar
  • Hintermüller M, Ito K, Kunisch K (2003) The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13(3):865–888.Google Scholar
  • Kumar Roy S, Mhammedi Z, Harandi M (2018) Geometry aware constrained optimization techniques for deep learning. Proc. IEEE Conf. CVPR (IEEE, Piscataway, NJ), 4460–4469.Google Scholar
  • Márquez-Neila P, Salzmann M, Fua P (2017) Imposing hard constraints on deep networks: Promises and limitations. Preprint, submitted June 7, https://arxiv.org/abs/1706.02025.Google Scholar
  • Na S, Anitescu M, Kolar M (2023) An adaptive stochastic sequential quadratic programming with differentiable exact augmented Lagrangians. Math. Programming 199(1):721–791.Google Scholar
  • Nandwani Y, Pathak A, Singla P (2019) A primal-dual formulation for deep learning with constraints. Adv. Neural Inform. Processing Systems 1091:12157–12168.Google Scholar
  • Nocedal J, Wright SJ (2006) Numerical Optimization, 2nd ed., Springer Series in Operations Research (Springer, New York).Google Scholar
  • Oztoprak F, Byrd R, Nocedal J (2023) Constrained optimization in the presence of noise. SIAM J. Optim. 33(3):2118–2136.Google Scholar
  • Paige CC, Saunders MA (1975) Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12(4):617–629.Google Scholar
  • Powell MJD (1978a) A fast algorithm for nonlinearly constrained optimization calculations. Watson GA, eds. Numerical Analysis, Lecture Notes in Mathematics, vol. 630 (Springer, Berlin, Heidelberg), 144–157.Google Scholar
  • Powell MJD (1978b) Algorithms for nonlinear constraints that use Lagrangian functions. Math. Programming 14(1):224–248.Google Scholar
  • Ravi SN, Dinh T, Lokhande VS, Singh V (2019) Explicitly imposing constraints in deep networks via conditional gradients gives improved generalization and faster convergence. Proc. Conf. AAAI Artificial Intelligence (AAAI Press, Palo Alto, CA), 4772–4779.Google Scholar
  • Rockafellar RT (1976) Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14(5):877–898.Google Scholar
  • Ruthotto L, Haber E (2020) Deep neural networks motivated by partial differential equations. J. Math. Imaging Vision 62:352–364.Google Scholar
  • Shapiro A, Dentcheva D, Ruszczyński A (2014) Lectures on Stochastic Programming: Modeling and Theory (SIAM, Philadelphia).Google Scholar
  • Sheriffdeen S, Ragusa JC, Morel JE, Adams ML, Bui-Thanh T (2019) Accelerating PDE-constrained inverse solutions with deep learning and reduced order models. Preprint, submitted December 17, https://arxiv.org/abs/1912.08864.Google Scholar
  • Shor NZ (2012) Minimization Methods for Non-Differentiable Functions, vol. 3 (Springer Science & Business Media, New York).Google Scholar
  • Summers T, Warrington J, Morari M, Lygeros J (2015) Stochastic optimal power flow based on conditional value at risk and distributional robustness. Internat. J. Electr. Power Energy Systems 72:116–125.Google Scholar
  • Tomar VS, Rose RC (2014) Manifold regularized deep neural networks. INTERSPEECH (ISCA, Singapore), 348–352.Google Scholar
  • Wilson RB (1963) A simplicial algorithm for concave programming. PhD thesis, Graduate School of Business Administration, Harvard University, Cambridge, MA.Google Scholar
  • Zhu Y, Zabaras N, Koutsourelakis PS, Perdikaris P (2019) Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data. J. Comput. Phys. 394:56–81.Google Scholar
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