Acceleration: G and F ∗ are both strongly convex
Majorization theorems for strongly convex functions
... 42. Xia, W.-F., Chu, Y.-M., Wang, G.-D.: Necessary and sufficient conditions for the Schur harmonic convexity or concavity of the extended mean values. Rev. Unión Mat. Argent. 52(1), 121–132 (2011) 43. Xia, ...
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Jensen–Steffensen inequality for strongly convex functions
... result Strongly convex functions have a very useful characterization: they always have a specific convex ...function f : I → R is strongly convex with modulus c if and only if the ...
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Revisiting Projection-Free Optimization for Strongly Convex Constraint Sets
... we both 1) show that FW can converge to a neigh- borhood of a global minimum, and 2) derive a convergence ...form f (w) := g(h(w)), where h is differentiable and monotonically increasing, and ...
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F G F Dynamics
... 3 Barotropic and Vortex Dynamics The ocean and atmosphere are full of vortices, i.e., locally recirculating flows with approximately circular streamlines and trajectories. Most of- ten the recirculation is in horizontal ...
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Catalyst Acceleration for First-order Convex Optimization: from Theory to Practice
... Beyond G¨ uler (1992), several works have inspired this ...grants acceleration to any optimization method, whereas the direct proof of Shalev- Shwartz and Zhang (2016), in the context of SDCA, does not ...
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On geodesic strongly E convex sets and geodesic strongly E convex functions
... geodesic strongly E-convex sets and geodesic strongly E-convex ...geodesic strongly E-convex sets are also ...in convex analysis and related optimization ...
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On the quadratic support of strongly convex functions
... Strongly convex functions were introduced by Polyak ...if f is strongly convex, then it is bounded from below, its level sets x ∈ I : f(x) ≤ λ are bounded for each λ and f ...
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Impulsive acceleration of strongly magnetized relativistic flows
... magnetic acceleration mechanism for such impulsive flows that can be much more effective than the acceleration of steady-state ...impulsive acceleration results in kinetic-energy-dominated flows that ...
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The pluricomplex Poisson kernel for strongly convex domains
... As a spin off result, using the properties of Ω D,p , we also prove that horospheres are (smooth and) strongly convex away from their center (see Theorem 4.1). The proofs of the previous properties of Ω D,p ...
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Acceleration Methods for Classic Convex Optimization Algorithms
... In the other direction, which is the one of interest here, there are also some results about the asymptotic number of support vectors as the number of samples grow, for example Steinwart (2003). Note that in theory the ...
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Some Properties of Generalized Strongly Harmonic Convex Functions
... harmonic convex functions with respect to an arbitrary trifunction F (·,·,·) : K ×K ×[0, 1] → R , which is called generalized strongly harmonic convex ...of strongly harmonic ...
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On Lower and Upper Bounds in Smooth and Strongly Convex Optimization
... Find min {ρ(q(z)) | q(z) is a real monic polynomial of degree p and q(1) = r} , (4) where r ∈ R and ρ(q(z)) denotes the maximum modulus over all roots of q(z). Although a vast range of techniques have been developed for ...
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Clayey Landslide Initiation and Acceleration Strongly Modulated by Soil Swelling
... measurements strongly suggested that variable pressure along the landslide ’s lateral shear boundaries resulting from seasonal soil expansion and contraction modulated its reactivation and ...
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THE CONVERGENCE OF BFGS METHOD UNDER STRONGLY CONVEX OPTIMIZATION PROBLEM
... 4.6.Line Search Strategies and Descents Methods[5] A line search algorithm searches for decrease in f in a descent direction. To compute the new step update in quasi-Newton methods one can use either the line ...
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INEQUALITIES VIA STRONGLY (p; h)-HARMONIC CONVEX FUNCTIONS
... Abstract. The main aim of this paper is to consider a new class of harmonic convex functions with respect to an arbitrary non-negative function, which is called strongly (p, h)-harmonic convex ...
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First-order methods with inexact oracle: the strongly convex case
... smooth strongly convex optimization, respectively the Primal Gradient Method (PGM), the Dual Gradient Method (DGM) and the Fast Gradient Method (FGM), when used with a (δ, L, ...smooth convex case, ...
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Convex ordered Γ-semi hypergroups associated to strongly regular relations
... of convex ordered Γ-semihypergroups associated to strongly regular ...a strongly regular relation on a convex ordered Γ-semihypergroup (S, Γ, ≤), then the quotient set (S/σ, Γ σ , ) is an ...
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Some Integral Inequalities of Simpson Type for Strongly Extended s Convex Functions
... for strongly extended s -convex ...of strongly extended s -convex function is ...of strongly extended s -convex function are ...
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Common boundary regular fixed points for holomorphic semigroups in strongly convex domains
... in some “admissible” subset of D (see Section 2 for precise definitions). In case D = D the unit disc of C, such admissible subsets are exactly the Stolz angles, and thus p ∈ ∂D is a boundary fixed point of f if ...
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Beyond the Regret Minimization Barrier: Optimal Algorithms for Stochastic Strongly-Convex Optimization
... convex cost functions that are also smooth, a O( T 1 ) rate is attainable by vanilla stochastic gradient descent (SGD), and further that SGD with special averaging of the last iterates recovers this optimal rate ...
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