scholarly journals On an algorithm in C 1,1 optimization

Filomat ◽  
2007 ◽  
Vol 21 (1) ◽  
pp. 17-24
Author(s):  
Nada Djuranovic-Milicic
Keyword(s):  
Rate Of Convergence ◽  
Directional Derivative ◽  
Second Order ◽  
Convergence Proof

In this paper an algorithm for minimization of C 1,1 functions, which uses the second order Dini upper directional derivative is considered. The purpose of the paper is to establish for this algorithm general hypotheses under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of convergence.

scholarly journals An algorithm for LC1 optimization

2005 ◽  
Vol 15 (2) ◽  
pp. 301-306 ◽  
Author(s):  
Nada Djuranovic-Milicic
Keyword(s):  
Rate Of Convergence ◽  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Directional Derivative ◽  
Second Order ◽  
General Algorithm ◽  
Unconstrained Optimization Problems ◽  
Convergence Proof

In this paper an algorithm for LC1 unconstrained optimization problems, which uses the second order Dini upper directional derivative is considered. The purpose of the paper is to establish general algorithm hypotheses under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of convergence.

scholarly journals A trust region algorithm for lc1 unconstrained optimization

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 285-290
Author(s):  
Nada Djuranovic-Milicic
Keyword(s):  
Rate Of Convergence ◽  
Unconstrained Optimization ◽  
Directional Derivative ◽  
Trust Region ◽  
Second Order ◽  
Trust Region Algorithm ◽  
Lipschitzian Functions ◽  
Convergence Proof ◽  
Locally Lipschitzian Functions

In this paper a trust region algorithm for minimization of locally Lipschitzian functions, which uses the second order Dini upper directional derivative is considered. A convergence proof is given, as well as an estimate of the rate of convergence. .

scholarly journals On an algorithm in nondifferential convex optimization

2013 ◽  
Vol 23 (1) ◽  
pp. 59-71
Author(s):  
Nada Djuranovic-Milicic ◽  
Milanka Gardasevic-Filipovic
Keyword(s):  
Convex Optimization ◽  
Objective Function ◽  
Directional Derivative ◽  
Second Order ◽  
Nondifferentiable Function ◽  
Convergence Proof ◽  
Yosida Regularization

In this paper an algorithm for minimization of a nondifferentiable function is presented. The algorithm uses the Moreau-Yosida regularization of the objective function and its second order Dini upper directional derivative. The purpose of the paper is to establish general hypotheses for this algorithm, under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of the convergence.

The Dunkl generalization of Stancu type q-Szasz-Mirakjan-Kantorovich operators and some approximation results

2018 ◽  
Vol 34 (3) ◽  
pp. 363-370
Author(s):  
M. MURSALEEN ◽  
◽  
MOHD. AHASAN ◽  
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Exponential Function ◽  
Second Order ◽  
Lipschitz Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
Kantorovich Operators ◽  
Korovkin’S Theorem

In this paper, a Dunkl type generalization of Stancu type q-Szasz-Mirakjan-Kantorovich positive linear operators ´ of the exponential function is introduced. With the help of well-known Korovkin’s theorem, some approximation properties and also the rate of convergence for these operators in terms of the classical and second-order modulus of continuity, Peetre’s K-functional and Lipschitz functions are investigated.

Almost-conservative second-order differential equations

1975 ◽  
Vol 77 (1) ◽  
pp. 159-169 ◽  
Author(s):  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Differential Equations ◽  
Rate Of Convergence ◽  
Second Order ◽  
Good Function ◽  
Second Order Differential Equations ◽  
Right Hand ◽  
Image Position ◽  
The Right

During the last thirty years an immense amount of research has been done on differential equations of the formwhere ε > 0 is small. It is usually assumed that the perturbing term on the right-hand side is a ‘good’ function of its arguments and that its dependence on t is purely trigonometric; this means that there is an expansion of the formwhere the ωn are constants, and that one may impose any conditions on the rate of convergence of the series which turn out to be convenient. Without loss of generality we can assumeand for convenience we shall sometimes write ω0 = 0. Often f is assumed to be periodic in t, in which case it is implicit that the period is independent of x and ẋ (We can also allow f to depend on ε, provided it does so in a sensible manner.)

Integrating Feature Direction Information with a Level Set Formulation for Image Segmentation

2016 ◽  
Vol 6 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Meng Li ◽  
Yi Zhan
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Directional Derivative ◽  
Image Features ◽  
Second Order ◽  
Directional Derivatives ◽  
Level Set Function ◽  
Variational Framework ◽  
Level Set Evolution ◽  
Level Set Formulation

AbstractA feature-dependent variational level set formulation is proposed for image segmentation. Two second order directional derivatives act as the external constraint in the level set evolution, with the directional derivative across the image features direction playing a key role in contour extraction and another only slightly contributes. To overcome the local gradient limit, we integrate the information from the maximal (in magnitude) second-order directional derivative into a common variational framework. It naturally encourages the level set function to deform (up or down) in opposite directions on either side of the image edges, and thus automatically generates object contours. An additional benefit of this proposed model is that it does not require manual initial contours, and our method can capture weak objects in noisy or intensity-inhomogeneous images. Experiments on infrared and medical images demonstrate its advantages.

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