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Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss.
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Neyman-pearson classification, convexity and stochastic constraints
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O (logt) projections for stochastic optimization of smooth and strongly convex functions
Zhang, L., Yang, T., Jin, R., and He, X · 2013
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Constrained optimization and Lagrange multiplier methods
Bertsekas, D. P · 2014
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On the complexity of finding first-order critical points in constrained nonlinear optimization
Cartis, C., Gould, N. I., and Toint, P. L · 2014
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Fairness constraints: Mechanisms for fair classification
Zafar, M. B., Valera, I., Rodriguez, M. G., and Gummadi, K. P · 2015
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Variance reduction for faster non-convex optimization
Allen-Zhu, Z. and Hazan, E · 2016
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Online convex optimization with stochastic constraints
Yu, H., Neely, M., and Wei, X · 2017
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From parity to preference-based notions of fairness in classification
Zafar, M. B., Valera, I., Rodriguez, M., Gummadi, K., and Weller, A · 2017
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Mirror descent and convex optimization problems with non-smooth inequality constraints
Bayandina, A., Dvurechensky, P., Gasnikov, A., Stonyakin, F., and Titov, A · 2018
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Universal stagewise learning for non-convex problems with convergence on averaged solutions
Chen, Z., Yang, T., Yi, J., Zhou, B., and Chen, E · 2018
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Efficiency of minimizing compositions of convex functions and smooth maps
Drusvyatskiy, D. and Paquette, C · 2018
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Optimal stochastic strongly convex optimization with a logarithmic number of projections
Chen, J., Yang, T., Lin, Q., Zhang, L., and Chang, Y · 2016
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Accelerated gradient methods for nonconvex nonlinear and stochastic programming
Ghadimi, S. and Lan, G · 2016
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Satisfying real-world goals with dataset constraints
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Convergence rate of frank-wolfe for non-convex objectives
Lacoste-Julien, S · 2016
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Algorithms for stochastic optimization with expectation constraints
Lan, G. and Zhou, Z · 2016
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Unified convergence analysis of stochastic momentum methods for convex and non-convex optimization
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Dc approach to weakly convex optimization and nonconvex quadratic optimization problems
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Catalyst for gradient-based nonconvex optimization
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Non-convex min-max optimization: Provable algorithms and applications in machine learning
Rafique, H., Liu, M., Lin, Q., and Yang, T · 2018
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Primal-dual frank-wolfe for constrained stochastic programs with convex and non-convex objectives
Wei, X. and Neely, M. J · 2018
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Solving non-smooth constrained programs with lower complexity than o ( 1 / ε ) o(1/\varepsilon) : A primal-dual homotopy smoothing approach
Wei, X., Yu, H., Ling, Q., and Neely, M · 2018
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Primal-dual stochastic gradient method for convex programs with many functional constraints
Xu, Y · 2018
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On the convergence rate of stochastic mirror descent for nonsmooth nonconvex optimization
Zhang, S. and He, N · 2018
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Optimization with convex and nonconvex functional constraints
Boob, D., Deng, Q., and Lan, G · 2019
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Almost surely constrained convex optimization
Fercoq, O., Alacaoglu, A., Necoara, I., and Cevher, V · 2019
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An inexact augmented lagrangian framework for nonconvex optimization with nonlinear constraints
Sahin, M. F., Alacaoglu, A., Latorre, F., Cevher, V., et al · 2019
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