scholarly journals Proximal Point Algorithms for Vector DC Programming with Applications to Probabilistic Lot Sizing with Service Levels

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Ying Ji ◽  
Shaojian Qu
Keyword(s):  
Global Convergence ◽  
Convex Functions ◽  
Lot Sizing ◽  
Dc Programming ◽  
Well Posedness ◽  
Proximal Point ◽  
Service Levels ◽  
Proximal Point Algorithms ◽  
Multicriteria Model ◽  
The Difference

We present a new algorithm for solving vector DC programming, where the vector function is a function of the difference of C-convex functions. Because of the nonconvexity of the objective function, it is difficult to solve this class of problems. We propose several proximal point algorithms to address this class of problems, which make use of the special structure of the problems (i.e., the DC structure). The well-posedness and the global convergence of the proposed algorithms are developed. The efficiency of the proposed algorithm is shown by an application to a multicriteria model stemming from lot sizing problems.

scholarly journals New Self-Adaptive Inertial-Like Proximal Point Methods for the Split Common Null Point Problem

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2316
Author(s):  
Yan Tang ◽  
Yeyu Zhang ◽  
Aviv Gibali
Keyword(s):  
Convergence Condition ◽  
Applied Science ◽  
Null Point ◽  
Point Problem ◽  
Proximal Point ◽  
Proximal Point Algorithms ◽  
The Difference ◽  
Further Development ◽  
Selection Of ◽  
Self Adaptive

Symmetry plays an important role in solving practical problems of applied science, especially in algorithm innovation. In this paper, we propose what we call the self-adaptive inertial-like proximal point algorithms for solving the split common null point problem, which use a new inertial structure to avoid the traditional convergence condition in general inertial methods and avoid computing the norm of the difference between xn and xn−1 before choosing the inertial parameter. In addition, the selection of the step-sizes in the inertial-like proximal point algorithms does not need prior knowledge of operator norms. Numerical experiments are presented to illustrate the performance of the algorithms. The proposed algorithms provide enlightenment for the further development of applied science in order to dig deep into symmetry under the background of technological innovation.

Successive coefficients of close-to-convex functions

2020 ◽  
Vol 32 (5) ◽  
pp. 1131-1141 ◽  
Author(s):  
Paweł Zaprawa
Keyword(s):  
Real Axis ◽  
Convex Functions ◽  
Positive Direction ◽  
The Real ◽  
Coefficient Problems ◽  
The Difference

AbstractIn this paper we discuss coefficient problems for functions in the class {{\mathcal{C}}_{0}(k)}. This family is a subset of {{\mathcal{C}}}, the class of close-to-convex functions, consisting of functions which are convex in the positive direction of the real axis. Our main aim is to find some bounds of the difference of successive coefficients depending on the fixed second coefficient. Under this assumption we also estimate {|a_{n+1}|-|a_{n}|} and {|a_{n}|}. Moreover, it is proved that {\operatorname{Re}\{a_{n}\}\geq 0} for all {f\in{\mathcal{C}}_{0}(k)}.

scholarly journals Formulations for dynamic lot sizing with service levels

2013 ◽  
Vol 60 (2) ◽  
pp. 87-101 ◽  
Author(s):  
Dinakar Gade ◽  
Simge Küçükyavuz
Keyword(s):  
Lot Sizing ◽  
Service Levels ◽  
Dynamic Lot Sizing

Refinements of the majorization-type inequalities via green and fink identities and related results

2018 ◽  
Vol 68 (4) ◽  
pp. 773-788 ◽  
Author(s):  
Sadia Khalid ◽  
Josip Pečarić ◽  
Ana Vukelić
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Cauchy Type ◽  
Linear Functionals ◽  
Ostrowski’S Inequality ◽  
New Family ◽  
Exponentially Convex Functions ◽  
The Difference

Abstract In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type inequality. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities.

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