New ways for comparing and bounding strongly (s,m)-convexfunctions using Caputo fractional derivatives and Caputo-Fabrizio integral operators are explored. These operators generalize some classic inequalities of Herm...
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New ways for comparing and bounding strongly (s,m)-convexfunctions using Caputo fractional derivatives and Caputo-Fabrizio integral operators are explored. These operators generalize some classic inequalities of Hermite-Hadamard for functions with strongly (s,m)-convex derivatives. The findings are also applied to special functions and means involving the digamma function. Additionally, we relate our findings to applications in biomedicine, engineering, robotics, the automotive industry, and electronics.
In this paper, we define a new class of strongly (g,h;alpha-m)-convexfunctions. Some important implications are listed and related with already known classes. Hermite-Hadamard-type inequalities are established for th...
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In this paper, we define a new class of strongly (g,h;alpha-m)-convexfunctions. Some important implications are listed and related with already known classes. Hermite-Hadamard-type inequalities are established for this new class of functions. Several particular cases are analysed. All the inequalities are established for Riemann-Liouville fractional integrals, and these are generalizations of ordinary integral inequalities.
In this paper, we introduce and investigate new classes of normalized analytic functions in an open unit disk with bounded radius and bounded boundary rotation by using the subordination. We discuss inclusion results,...
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In this paper, we introduce and investigate new classes of normalized analytic functions in an open unit disk with bounded radius and bounded boundary rotation by using the subordination. We discuss inclusion results, co-efficient bounds, growth and distortion theorems of the classes. Moreover, we compute the radii of strong starlikeness, convexity and starlikeness of the classes. It is interesting to mention that most of our findings are best possible as compared to the existing results in the literature.
In the article, we present several majorization theorems for strongly convex functions and give their applications in inequality theory. The given results are the improvement and generalization of the earlier results.
In the article, we present several majorization theorems for strongly convex functions and give their applications in inequality theory. The given results are the improvement and generalization of the earlier results.
New characterizations of inner product spaces among normed spaces involving the notion of strong convexity are given. In particular, it is shown that the following conditions are equivalent: (1) (X, parallel *** to) i...
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New characterizations of inner product spaces among normed spaces involving the notion of strong convexity are given. In particular, it is shown that the following conditions are equivalent: (1) (X, parallel *** to) is an inner product space;(2) f : X -> R is stronglyconvex with modulus c > 0 if and only if f - c parallel *** to(2) is convex;(3) parallel *** to(2) is stronglyconvex with modulus 1.
We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in V (Adv Comput Math 38(3):667-681, 2013) for solving monotone inclusion problems. Under strong m...
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We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in V (Adv Comput Math 38(3):667-681, 2013) for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators involved we obtain for the sequences of iterates that approach the solution orders of convergence of and , for , respectively. The investigated primal-dual algorithms are fully decomposable, in the sense that the operators are processed individually at each iteration. We also discuss the modified algorithms in the context of convex optimization problems and present numerical experiments in image processing and pattern recognition in cluster analysis.
作者：
Li, XiuxianXie, LihuaHong, YiguangInst Adv Study
Dept Control Sci & Engn Coll Elect & Informat Engn Shanghai 201804 Peoples R China Tongji Univ
Shanghai Res Inst Intelligent Autonomous Syst Shanghai 201804 Peoples R China Nanyang Technol Univ
Sch Elect & Elect Engn Singapore 639798 Singapore Tongji Univ
Coll Elect & Informat Engn Dept Control Sci & Engn Shanghai 201804 Peoples R China
This article proposes a new framework for distributed optimization, called distributed aggregative optimization, which allows local objective functions to be dependent not only on their own decision variables, but als...
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This article proposes a new framework for distributed optimization, called distributed aggregative optimization, which allows local objective functions to be dependent not only on their own decision variables, but also on the sum of functions of decision variables of all the agents. To handle this problem, a distributed algorithm, called distributed aggregative gradient tracking, is proposed and analyzed, where the global objective function is stronglyconvex, and the communication graph is balanced and strongly connected. It is shown that the algorithm can converge to the optimal variable at a linear rate. A numerical example is provided to corroborate the theoretical result.
We consider the linearly constrained separable convex minimization problem, whose objective function consists of the sum of individual convexfunctions in the absence of any coupling variables. While augmented Lagrang...
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We consider the linearly constrained separable convex minimization problem, whose objective function consists of the sum of individual convexfunctions in the absence of any coupling variables. While augmented Lagrangian-based decomposition methods have been well developed in the literature for solving such problems, a noteworthy requirement of these methods is that an additional correction step is a must to guarantee their convergence. This note shows that a straightforward Jacobian decomposition of the augmented Lagrangian method is globally convergent if the involved functions are further assumed to be stronglyconvex.
Schauder's fixed point theorem and the Banach contraction principle are used to study an iterative functional equation. We give sufficient conditions for the existence, uniqueness, and stability of the strongly co...
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Schauder's fixed point theorem and the Banach contraction principle are used to study an iterative functional equation. We give sufficient conditions for the existence, uniqueness, and stability of the stronglyconvex and strongly concave solutions. We also give the approximate sequences for the corresponding solutions. Finally, some examples are considered for our results.
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