Convex Optimization in Normed Spaces: Theory, Methods and Examples

By Juan Peypouquet. 2015

163 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/194ca9d4118ccb3689ec72a3ab7dca6144c51b55

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Citations in the corpus

The Balancing Act in Causal Inference (2021, background): “(32) Here, ζ∗(y) = supx xy−ζ(x) is the convex conjugate of the function ζ (see, e.g., Peypouquet, 2015).”
From error bounds to the complexity of first-order descent methods for convex functions (2015, methodology): “It is classical to see that for any x̂ ∈ C, the sequence ‖xk − x̂‖ is decreasing (see, for instance, [58]).”
Rate of convergence of the Nesterov accelerated gradient method in the subcritical case α ≤ 3 (2017, unknown): “6) proxγΨ(x) = argminξ∈H ˆ Ψ(ξ)+ 1 2γ kξ −xk2 ˙ = (I +γ∂Ψ)−1 (x). This last equality expresses that proxγΨ is the resolvent of index γ of the maximal monotone operator ∂Ψ. One can consult [11], [29], [30], [31] for a recent account on the proximal-based splitting methods. a) For α = 3, we recover th”
The Rate of Convergence of Nesterov's Accelerated Forward-Backward Method is Actually Faster Than 1/k2 (2015, unknown): “For standard convex analysis background, see [3, 22].”
Augmented minimax linear estimation (2017, methodology): “…recall that, by the Riesz representation theorem, any continuous linear functional ψ(·) on the square integrable functions from Z to R has a Riesz representer γψ(·), i.e., a function satisfying E [γψ(Zi)f(Zi)] = ψ(f) for all square-integrable functions f (see e.g. Peypouquet, 2015, Theorem 1.4.1).”
On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning (2017, background): “Most of the proofs of the propositions in this section can be found in references such as [7], [24], [25], [26], [27], [28].”