Nonlinear Programming

By Osman Güler. 2010

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Citations in the corpus

Reinforcement learning in robotics: A survey (2013, positive): “Using the property ∑ s′,a′ V ( s ′)μπ ( s′)π ( s′, a′) = ∑s,a V ( s)μπ ( s)π ( s, a), we can obtain the Karush–Kuhn– Tucker conditions (Kuhn and Tucker, 1950) by differentiating with respect to μπ (s)π (s, a) which yields extrema at ∂μππL = R(s, a) + ∑ s′ Vπ (s′) T(s, a, s′) −R̄ − Vπ ( s) = 0.”
Distributed Alternating Direction Method of Multipliers (2012, neutral): “The optimality implies there exists some subgradient h(x i ) in ∂fi(x k+1 i ) such that h(x k+1 i ) +∇g i (x k+1 i ) = 0 [1], and thus (xi − x i )′[h(x k+1 i ) + ∇g i (x k+1 i )] = 0 for all xi in R.”
Weakly-Supervised Alignment of Video with Text (2015, neutral): “First, note that Y is the convex hull of Y , and the solution to minY ∈Y Tr(AY ) is also a solution of minY ∈Y Tr(AY ) [5].”
Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learning (2014, positive): “For general non-convex problems, proving convergence to a global (or local) minimum is impossible in general, and classical analysis studies instead asymptotic stationary point conditions (see, e.g., [4]).”
Learning Discrete Representations via Information Maximizing Self-Augmented Training (2017, positive): “We use the penalty method (Bertsekas, 1999) to solve the optimization.”
Estimating the Spectral Density of Large Implicit Matrices (2018, neutral): “In dynamical systems, numerical algorithms, and control, eigenstructure helps us analyze local stability and typical behaviors (Luenberger, 1979; Bertsekas, 2016).”
Distributed subgradient methods and quantization effects (2008, neutral): “1For subgradient methods see, for example, [19], [22], [20], [8], [1], [2].”
Online Learning for Matrix Factorization and Sparse Coding (2009, positive): “It does not ensure the convergence of D t , but guarantees the convergence of the positive sum P F , a classical condition in gradient descent convergence proofs (Bertsekas, 1999).”
A Unified Convergence Analysis of Block Successive Minimization Methods for Nonsmooth Optimization (2012, neutral): “In fact, as we will see later in this paper, successively optimizing an approximat e version of the original objective is the key idea of many important algorithms such as the concave-conve x procedure [33], the EM algorithm [10], the proximal minimization algorithm [2], to name a few.”
Multi-Task Learning as Multi-Objective Optimization (2018, neutral): “These methods use multi-objective Karush-Kuhn-Tucker (KKT) conditions (Kuhn and Tucker, 1951) and ﬁnd a descent direction that decreases all objectives.”