On solving constrained optimization problems with neural networks: a penalty method approach

By W. E. Lillo, M. Loh, S. Hui, Stanislaw H. Zak. 1993

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Citations in the corpus

OptNet: Differentiable Optimization as a Layer in Neural Networks (2017, background): “Indeed, the general idea of solving restricted classes of optimization problem using neural networks goes back many decades (Kennedy & Chua, 1988; Lillo et al., 1993), but has seen a number of advances in recent years.”
Learning Generative Adversarial RePresentations (GAP) under Fairness and Censoring Constraints (2019, methodology): “To incorporate the distortion constraint, we use the penalty method Lillo et al. [1993] to replace the constrained optimization problem by adding a penalty to the objective function.”
Context-Aware Generative Adversarial Privacy (2017, methodology): “For convex optimization problems, the solution to the series of unconstrained problems will eventually converge to the solution of the original constrained problem [92].”
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism (2020, unknown): “i, but are adaptively updated by the neural network training procedure. We remark that the use of neural networks to solve penalty-based constrained optimization problems has been proposed previously [18, 19] but not using trainable weights, as far as we know. The gradient ascent/descent step can be”
Censored and Fair Universal Representations using Generative Adversarial Models (2019, methodology): “To incorporate the distortion constraint into the learning algorithm, we use the penalty method [Lillo et al., 1993] and augmented Lagrangian method [Eckstein and Yao, 2012] to replace the constrained optimization problem by a series of unconstrained problems whose solutions asymptotically converge ”
Generative Adversarial Privacy: A Data-Driven Approach to Information-Theoretic Privacy (2018, methodology): “To incorporate the distortion constraint, we use the penalty method [18] to replace the constrained optimization problem by adding a penalty to the objective function.”