Mathematical Theory of Optimal Processes

By Richard Bellman, L. Pontryagin, V. Boltyanskii, R. Gamkrelidze, E. Mischenko. 1962

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In Mathematical Optimization

Citations in the corpus

Neural Ordinary Differential Equations (2018, positive): “We treat the ODE solver as a black box, and compute gradients using the adjoint sensitivity method (Pontryagin et al., 1962).”
StyleFlow: Attribute-conditioned Exploration of StyleGAN-Generated Images using Conditional Continuous Normalizing Flows (2020, background): “Radford et al. (2016) observed that interesting semantic editing operations can be achieved by rst computing a dierence vectors between two latent codes (e.”
Path integrals and symmetry breaking for optimal control theory (2005, methodology): “ovement in biological systems, robotics, and ﬁnancial investment policies. In the absence of noise, the optimal control problem can be solved in two ways: using the Pontryagin Minimum Principle (PMP) [1] which is a pair of ordinary diﬀerential equations that are similar to the Hamilton equations of ”
Data-Efficient Reinforcement Learning with Probabilistic Model Predictive Control (2017, background): “d Results Bellman’s optimality principle[1] yields a recursive formulation for calculating the total expected cost (2) and gives a sufﬁcient optimality condition. Pontryagin’s Maximum Principle (PMP) [32] provides the corresponding necessary optimality condition. The PMP allows us to compute gradien”
Switching Time Optimization for Bang-Bang and Singular Controls (2010, background): “[13] are well-known.”
Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control (2009, background): “For a proof of the maximum principle and further references see, e.g., [9, 29 ].”
A Study of Reinforcement Learning in the Continuous Case by the Means of Viscosity Solutions (2000, methodology): “The two possible approaches for optimal control are Pontryagin’smaximum principle (for theoretical work, see Pontryagin et al. (1962) and more recently Fleming and Rishel (1975), for a study of Temporal Difference, see Doya (1996), and for an application to the control with neural networks, see Be”
Data-driven discovery of Koopman eigenfunctions for control (2017, methodology): “Generally applicable frameworks, such as dynamic programming [15], Pontryagin’s maximum principle [92], and model-predictive control (MPC) [2, 26], often suffer from the curse of dimensionality and require considerably computational effort, e.”
Needle Variations in Infinite-Horizon Optimal Control (2014, background): “To our knowledge for the first time a version of the maximum principle for the infinitehorizon optimal control problem was proved in [16] in the case when the improper integral utility functional converges and the optimal trajectories satisfy additional boundary constraint limt→∞ x∗(t) = x1, where x”