First-order condition for a convex function f
A Note on Convex Transformations and the First Order Approach
... The first order approach to solving the standard one-dimensional principal-agent model is conditional upon the relevant stochastic production function obeying two noteworthy restrictions: that the ...
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Stochastic first order methods in smooth convex optimization
... efficient first-order methods for convex optimization problems in the simultaneous presence of smoothness of the objective function and stochasticity in the first-order ...
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First-order methods of smooth convex optimization with inexact oracle
... different first-order methods of smooth convex optimization employing inexact first-order ...approximate first-order ...objective function and the accuracy of the ...
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First-order methods with inexact oracle: the strongly convex case
... three first-order methods of 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 ...
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A first-order primal-dual algorithm for convex problems with applications to imaging
... classes: Convex and non-convex problems. The advantage of convex problems over non-convex problems is that a global optimum can be computed, in general with a good precision and in a ...
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Diagonal preconditioning for first order primal-dual algorithms in convex optimization
... tive function as δ k = |E ∗ − E k |/|E ∗ |, where E ∗ refers to the optimal value and E k is the value of the current ...In order to deter- mine the optimal value of the objective function we run one ...
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Catalyst Acceleration for First-order Convex Optimization: from Theory to Practice
... descent condition, which, when satisfied, grants acceleration to any optimization method, whereas the direct proof of Shalev- Shwartz and Zhang (2016), in the context of SDCA, does not extend to non-strongly ...
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Potential-Function Proofs for First-Order Methods
... potential function is also known to the specialists; ...potential function we use in § 5.2 . However, these potential function proofs and intuitions have ...
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Hermite–Hadamard type inequalities for F convex function involving fractional integrals
... For more recent results on integral inequalities of Hermite–Hadamard type concerning the F -convex functions, we refer the interested reader to [19] and the references therein. In the sequel, we recall the ...
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First order optimality condition for constrained set-valued optimization
... 1 t F (x 0 + tu) − y 0 . (4) The definitions of a derivative of a set-valued map are introduced in different ways, see e.g. [1, 4, 14]. Many of them are defined geometrically. Among the others, because of its ...
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On the Relationship between Conjugate Gradient and Optimal First-Order Methods for Convex Optimization
... of first-order methods makes this class of algorithms a pop- ular choice and an efficient technique for solving large-scale ...strongly convex functions has remained open for ...
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From error bounds to the complexity of first-order descent methods for convex functions
... Dedicated to Jean-Pierre Dedieu who was of great inspiration to us. Abstract This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in ...
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Representations of first order function types as terminal coalgebras
... In the current form our result is not applicable to categories of constructive functions like ω-Set. However, it seems likely that our result still holds when moving to an appropriate internal notion of limits and ...
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Harmonic mappings for which co analytic part is a close to convex function of order b
... starlike function in the unit disc ...monic function f , which maps D onto some planar domain f ...mapping f has a canonical decomposition f = h + g, where h(z) and g(z) are ...
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Theorem 1. A real valued function on a convex set Kin RRRR is a convex function if
... ≥ f ( x 1 , x 2 , ... , x k ) where f is a first degree polynomial in the coordinates x j and k = 1 or 2 depending upon whether we are looking at R R R R 2 or R R R R 3 ...other convex sets ...
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Imputing a Convex Objective Function
... objective function, we can use it to predict the production level and edge flows for a given demand ...the convex optimization problem (6) and dynami- cally adjust the consumer prices by using ν p+1 , ...
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An optimal first-order primal-dual gap reduction framework for constrained convex optimization
... optimal first-order primal-dual methods for the prototypical constrained convex optimization tem- ...in first-order primal-dual algorithms must compete with their constraint feasibil- ...
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First order function dispatch in a Java like programming language
... 5.2. Performance The prototype is designed to show the semantics of Co-op, not to be an efficient imple- mentation of the Co-op runtime. Therefore, the prototype might use more memory and processing power than expected ...
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Estimating a convex function in nonparametric regression
... We first estimate the derivative of the regression function, which is isotonized in a second step to obtain a strictly isotone and smooth estimate of the derivative of the regression ...strictly ...
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Estimating a Convex Function in Nonparametric Regression
... a convex regression function is proposed and its stochastic properties are ...regression function, which is firstly isotonized and then ...is first order asymptotically equivalent to ...
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