Nonlinear Programming

By J. Killen. 2021

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In Mathematical Optimization

Citations in the corpus

Fast and Furious Convergence: Stochastic Second Order Methods under Interpolation (2019, methodology): “Bertsekas (1997) shows that the Gauss-Newton method is equivalent to Newton’s method for solving nonlinear least-squares when interpolation is satisﬁed; hence the convergence is also superlinear.”
A Tight and Unified Analysis of Extragradient for a Whole Spectrum of Differentiable Games (2019, methodology): “This point of view was presented in Polyak (1987); Bertsekas (1999) and recently used in Arjevani et al. (2016); Mescheder et al. (2017); Gidel et al. (2019b) for instance.”
Gradient-Based Neural DAG Learning (2019, methodology): “Nevertheless, a standard numerical solver for constrained optimization such has an augmented Lagrangian method (AL) [1] can be applied to get an approximate solution.”
Negative Momentum for Improved Game Dynamics (2018, methodology): “4.4.1 Bertsekas (1999)) .”
Robust Aggregation for Federated Learning (2019, neutral): “[9] D.”
Differentiable Model Compression via Pseudo Quantization Noise (2021, methodology): “Then, following the exact penalty method (Bertsekas (1997), Section 4.2, Bertsekas (2014), Chapter 4), there is λ(m) > 0 (or λ(l) for the right hand side problem), such that the left hand size problem is equivalent to”
Reinforcement Learning via Fenchel-Rockafellar Duality (2020, background): “Danskin’s theorem (Bertsekas, 1999) tells us that where , d ; π ).”
AlgaeDICE: Policy Gradient from Arbitrary Experience (2019, methodology): “By taking the gradient of J D ,f with respect to x and setting this to 0, one ﬁnds that (17) Thus, we may express the gradient of where we have used Danskin’s theorem (Bertsekas, 1999) to ignore gradients of π through ν ∗ π .”
Imitation Learning via Off-Policy Distribution Matching (2019, background): “…matching objective for π as a max - min optimization: If the inner objective over ν is sufﬁciently optimized, the gradients of π may be computed directly (Bertsekas, 1999), noting that, In continuous control environments when π is parameterized by a Gaussian and ν is a neural network, one may…”
DAG-GNN: DAG Structure Learning with Graph Neural Networks (2019, methodology): “For completeness, we summarize the algorithm here; the reader is referred to standard textbooks such as Section 4.2 of Bertsekas (1999) for details and convergence analysis.”
A Sufficient Condition for Convergences of Adam and RMSProp (2018, background): “Due to the uncertainty of distribution P, the batch gradient descent algorithm [4] is impractical to employ full gradient ∇f(x) to solve problem (1).”
Masked Gradient-Based Causal Structure Learning (2019, methodology): “The choices of h i include polynomial functions and MLPs. Augmented Lagrangian method consists of optimizing a sequence of subproblems where the exact solutions converge to a stationary point of the original constrained problem under some regularity conditions [2].”
Weighted Sum-Rate Maximization for Reconfigurable Intelligent Surface Aided Wireless Networks (2019, methodology): “We design the step size κ can be determined by the Armijo rule [51]:”
Private Weighted Random Walk Stochastic Gradient Descent (2020, methodology): “For convergence guarantees [23], we use a decreasing step size that satisfies ∞ ∑”
Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks (2020, methodology): “As this condition number gets smaller, the convergence rate of the objective value can improve when the matrix M is normal [18].”
Differentiable Neural Architecture Search via Proximal Iterations (2019, background): “The benefit of such idea is that a differentiable space enables computation of gradient information, which could speed up the convergence of underneath optimization algorithm [5].”