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This paper introduces a distributed continuous-time algorithm that utilizes dual consensus to tackle the optimization problem involving time-varying (TV) local objective functions and TV coupled equality constraint. Here, the local objective functions can be any strongly convex functions. The optimum solution is represented by a trajectory rather than a fixed point, owing to the dynamic nature of the objective functions and the constraint. The initial step involves converting the studied problem into an equivalent saddle-point problem. Subsequently, we provide the optimal conditions for this transformed problem. Then a distributed continuous-time algorithm based on dual consensus is provided, guaranteeing that all agents possess the capability to discover and follow the optimal TV trajectories. It is noticeable that there are no limitations imposed on the information regarding local objective functions and the coupled equality constraint except for the strongly convexity of local objective functions. In addition, two simulation instances and the comparisons with state-of-the-art methods are performed in order to validate the proposed algorithm. • Dual consensus method is designed to address the time-varying optimization with coupled equality constraint. • The algorithm allows more flexibility for the local objective functions. • Bound restrictions on the information about local objective functions and the coupled equality constraint are removed. • The algorithm guarantees vanishing tracking errors. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the stability problem is investigated for a class of discrete-time switched systems with unstable subsystems under the mode-dependent average dwell time (MDADT) switching. A multiple convex Lyapunov function (MCLF) and a multiple piecewise convex Lyapunov function (MPCLF) are firstly proposed, which are formulated in a convex combination form of positive definite matrices with quasi-time-dependent coefficients. It is pointed out in the paper that the multiple Lyapunov function (MLF) and the multiple discontinuous Lyapunov function (MDLF) can be regarded as special cases of the proposed MCLF and MPCLF, respectively. Then, the exponential stability conditions are derived by the new Lyapunov functions. Both slow switching and fast switching are exerted on stable modes and unstable modes, respectively. Finally, two numerical examples are given to demonstrate that larger stability regions and tighter MDADT bounds can be obtained by using our developed techniques compared with some recent results. [ABSTRACT FROM AUTHOR]

In this paper, we show the connections of inequalities involving fractional integrals with Ohlin lemma and Levin-Stechkin theorem. First, we give a new proof of the fractional version of the inequality of Hermite Hadamard type and then we extend it in two directions. Thus we compare the fractional expression occurring in this inequality with the usual integral and we obtain stronger inequalities (one of them is related to Bullen inequality). • The use of stochastic orderings tools in the theory of inequalities for fractional integrals. • A new proof of the fractional version of the Hermite-Hadamard inequality. • Inequalities between the fractional integral and the regular one. • Refinements of Hermite-Hadamard inequality (in particular a fractional version of Bullen inequality). [ABSTRACT FROM AUTHOR]

• Establishment of a power-gas network system model for efficient energy absorption and smart grid load shifting. • Introduction of a novel ADMM-based cooperative regulation scheme, enhancing convergence through dynamic step size adjustment. • Development of an improved cooperative scheme, addressing inequality constraints with privacy guarantees and flexible initial conditions. This paper considers the optimal capacity allocation of integrated energy systems (IESs) with the power-gas systems for clean energy consumption. First, power-gas network models are established with equality and inequality constraints. Second, a novel full distributed cooperative optimal regulation scheme is designed to deal with the optimal capacity allocation problem. Moreover, to deal with the inequality constraints in IESs, a distributed projection operator is developed such that the system states can be guaranteed within the constraint conditions. Then the convergences of those distributed optimization algorithms were proved for strictly convex objective functions. And the initial conditions of systems for the algorithm are free. The simulation is provided to demonstrate the effectiveness of the distributed optimazation approach. [ABSTRACT FROM AUTHOR]

The distributed task allocation problem, as one of the most interesting distributed optimization challenges, has received considerable research attention recently. Previous works mainly focused on the task allocation problem in a population of individuals, where there are no constraints for affording task amounts. The latter condition, however, cannot always be hold. In this paper, we study the task allocation problem with constraints of task allocation in a game-theoretical framework. We assume that each individual can afford different amounts of task and the cost function is convex. To investigate the problem in the framework of population games, we construct a potential game and calculate the fitness function for each individual. We prove that when the Nash equilibrium point in the potential game is in the feasible solutions for the limited task allocation problem, the Nash equilibrium point is the unique globally optimal solution. Otherwise, we also derive analytically the unique globally optimal solution. In addition, in order to confirm our theoretical results, we consider the exponential and quadratic forms of cost function for each agent. Two algorithms with the mentioned representative cost functions are proposed to numerically seek the optimal solution to the limited task problems. We further perform Monte Carlo simulations which provide agreeing results with our analytical calculations. • Distributed task allocation problem is studied by using a game-theoretical approach. • We construct a potential game to calculate the fitness function for each individual. • The Nash equilibrium point is proved to be the unique globally optimal solution. • Typical cost functions are used to support our theoretical analysis via Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the composite convex minimization problem where the cost function consists of a smooth convex function with Lipschitz gradient and a closed proper convex function with non-polyhedral epigraph. For this class of non-polyhedral convex optimization problems, we establish the locally Lipschitzian type error bounds for estimating the distance to the solution set from any feasible point near the solution set, and the globally Lipschitzian type error bounds for the smooth function with a special structure, with the help of the local weak sharpness of minima or the calmness of appropriate multifunctions, and also provide verifiable regularity conditions to guarantee them to hold. Although the derived local error bounds are weaker than the one used in Luo and Tseng (1992,1993) and Wei and Jen (2014), when applying them to an inexact feasible descent method (FDM) and proximal gradient method (PGM), respectively, we still achieve the asymptotic Q -linear convergence and R -linear convergence of the objective value sequence and the iterate sequence, respectively. As an illustration of these results, we obtain the linear convergence of the PGM for the trace norm regularized least squares problem under a regularity condition of the linear operator. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we generalize the classical primal–dual logarithmic barrier method for linear optimization to convex quadratic optimization over symmetric cone by using Euclidean Jordan algebras. The symmetrization of the search directions used in this paper is based on the Nesterov–Todd scaling scheme, and only full Nesterov–Todd step is used at each iteration. We derive the iteration bound that matches the currently best known iteration bound for small-update methods, namely, . Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm. [Copyright &y& Elsevier]

Abstract This paper improves a decomposition-like proximal point algorithm, developed for computing minima of nonsmooth convex functions within a framework of symmetric positive semidefinite matrices, and extends it to domains of positivity of reducible type, in a nonlinear sense and in a Riemannian setting. Several computational experiments with weighted Lp (p = 1 , 2) centers of mass are performed to demonstrate the practical feasibility of the method. [ABSTRACT FROM AUTHOR]

Abstract: On the assumption that investment fund follows the logarithm-normal distribution, the paper derives the forms of proportional and excess-of-loss reinsurance contracts which make the convex combination of the insurer’s rate of return v 1 and the reinsurer’s rate of return v 2 exceeds R at the probability of f. In the whole paper, the premium takes the expectation principle. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to investigate various properties and characteristics of the Dziok–Srivastava operator introduced in Dziok and Srivastava [J. Dziok, H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999) 1–13]. Our paper is motivated essentially by the familiar work Liu and Srivastava [J.-L. Liu, H.M. Srivastava, Certain properties of the Dziok–Srivastava operator, Appl. Math. Comput. 159 (2004) 485–493] which has been recently published. [Copyright &y& Elsevier]

• The proposed Prox-NPGA can handle the non-smooth term in the objective function. • The convergences of CTA-Prox-NPGA and ATC-Prox-NPGA are proved. • The upper bounds of the step-sizes are given. • Prox-NPGA is not only an algorithm, but also an algorithmic framework. In this paper, we study a class of distributed constraint-coupled optimization problems, where each local function is composed of a smooth and strongly convex function and a convex but possibly non-smooth function. We design a novel proximal nested primal-dual gradient algorithm (Prox-NPGA), which is a generalized version of the exiting algorithm–NPGA. The convergence of Prox-NPGA is proved and the upper bounds of the step-sizes are given. Finally, numerical experiments are employed to verify the theoretical results and compare the convergence rates of different versions of Prox-NPGA. [ABSTRACT FROM AUTHOR]

This paper presents a canonical d.c. (difference of canonical and convex functions) programming problem, which can be used to model general global optimization problems in complex systems. It shows that by using the canonical duality theory, a large class of nonconvex minimization problems can be equivalently converted to a unified concave maximization problem over a convex domain, which can be solved easily under certain conditions. Additionally, a detailed proof for triality theory is provided, which can be used to identify local extremal solutions. Applications are illustrated and open problems are presented. [ABSTRACT FROM AUTHOR]

The authors deduce a differentiable mapping integral identity with two parameters. Using this integral identity, this paper establishes new inequalities of Simpson type for extended ( s, m )-convex functions under certain conditions. This contributes to new better estimates than the earlier results. Finally, these inequalities are applied to special means. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate several new subclasses of close-to-convex functions and their related mappings. Various interesting properties including sufficiency criteria, coefficient estimates, arc-length problem and radius of convexity are investigated. [ABSTRACT FROM AUTHOR]

In this paper, a new general identity for fractional integrals have been defined. By using of this identity, new estimates on generalization of Hadamard, Ostrowski and Simpson like type inequalities for harmonically quasi-convex functions via the Riemann–Liouville fractional integral have been obtained. [ABSTRACT FROM AUTHOR]

A spline space suitable for Isogeometric Analysis (IgA) on multi-patch domains is presented. Our construction is motivated by emerging requirements in isogeometric simulations. In particular, IgA spaces should allow for adaptive mesh refinement and they should guarantee the optimal smoothness of the discretized solution, even across interfaces of adjacent patches. Given a domain manifold M consisting of individual patches (isomorphic to the unit square or cube) that are glued together along interfaces, we present a construction of multi-patch B-splines defined on them. Their smoothness is enhanced by locally modifying or merging basis functions around the boundary of each patch. The resulting multi-patch B-splines with enhanced smoothness (MPBES) possess the property of local linear independence and form a non-negative partition of unity. Moreover, their span can be characterized as the linear space of all piecewise polynomial functions on the domain manifold that possess certain smoothness properties. Subsequently, adaptively refined MPBES are obtained by generalizing the construction of truncated hierarchical (TH) B-splines. More precisely, a nested sequence of spaces spanned by MPBES is considered, corresponding to steps of local enrichment. In addition, an inversely nested sequence of subdomains (which are submanifolds of M ) is used to specify the local refinement level of functions in these spaces. Finally, truncated hierarchical MPBES are obtained by means of the selection and truncation mechanism of THB-splines. The desired properties of linear independence and convex partition of unity are maintained. The paper presents several numerical examples which demonstrate potential applications of the new basis in isogeometric analysis. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to give extensions of the Hermite–Hadamard inequality for harmonically convex functions via Riemann–Liouville fractional integrals. We show how to relax the harmonically convexity property of the function f . Obtained results in this work involve a larger class of functions. Our results are the refinements of the existing results for harmonically convex functions. [ABSTRACT FROM AUTHOR]

It is widely known that the sum of the angles of a triangle equals two right angles. Far less known are the answers to similar questions for tetrahedra and higher dimensional simplices. In this paper we review some of these less known results, and look at them from a different point of view. Then we continue to derive tight bounds on the dihedral angle sums for the subclass of nonobtuse simplices. All the dihedral angles of such simplices are less than or equal to right. They have several important applications (Brandts et al., 2009). The main conclusion is that when the spatial dimension n is even, the range of dihedral angle sums of nonobtuse simplices is n times smaller than the corresponding range for arbitrary simplices. When n is odd, it is n - 1 times smaller. [ABSTRACT FROM AUTHOR]

The class of bounded radius of rotation is generalization of the convex functions. The concept of functions bounded boundary rotation originated from Loewner (1917). But he did not use the present terminology. It was Paatero (1931, 1933) who systematically developed their properties and made an exhaustive study of the class V k . In the present paper we will investigate the class of harmonic mappings which is related to the class of bounded boundary rotation. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and investigate a certain new subclass MK ( λ , t , A , B ) of meromorphic close-to-convex functions. Some results such as inclusion relationship, coefficient inequality and some property for this class are derived. The results obtained here are extension of earlier known work. [ABSTRACT FROM AUTHOR]

This paper focuses on deriving an improved stability criterion for discrete time-delay systems via a Lyapunov–Krasovskii functional approach that takes advantage of triple summation terms. To this end, novel convex combination coefficients coupled with second-order time-varying delay terms are introduced, and the corresponding reciprocally convex approach is established with the use of the minimal number of slack matrix variables. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed method, with particular regard to robustness and H ∞ performance. [ABSTRACT FROM AUTHOR]

In the present paper we establish several fuzzy differential subordinations regarding the operator L α m , given by L α m : A → A , L α m f ( z ) = ( 1 − α ) R m f ( z ) + α S m f ( z ) , where R m f ( z ) denote the Ruscheweyh derivative, S m f ( z ) is the Sălăgean operator and A n = { f ∈ H ( U ) , f ( z ) = z + a n + 1 z n + 1 + ⋯ , z ∈ U } is the class of normalized analytic functions with A 1 = A . A certain fuzzy class, denoted by S L F m ( δ , α ) , of analytic functions in the open unit disk is introduced by means of this operator. By making use of the concept of fuzzy differential subordination we will derive various properties and characteristics of the class S L F m ( δ , α ) . Also, several fuzzy differential subordinations are established regarding the operator L α m . [ABSTRACT FROM AUTHOR]

In this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite–Hadamard–Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works. [ABSTRACT FROM AUTHOR]

This paper investigates existence of PC -mild solutions of impulsive fractional differential inclusions with nonlocal conditions when the linear part is a fractional sectorial operators like in Bajlekova (2001) [1] on Banach spaces. We derive two existence results of PC -mild solutions when the values of the semilinear term F is convex as well as another existence result when its values are nonconvex. Further, the compactness of the set of solutions is characterized. [ABSTRACT FROM AUTHOR]

In this paper we define purely iterative algorithm for Newton’s maps which is a slight modification of the concept of purely iterative algorithm due to Smale. For this, we use a characterization of rational maps which arise from Newton’s method applied to complex polynomials. We prove the Scaling Theorem for purely iterative algorithm for Newton’s map. Then we focus our study in dynamical aspects of three root-finding iterative methods viewed as a purely iterative algorithm for Newton’s map: Whittaker’s iterative method, the super-Halley iterative method and a modification of the latter. We give a characterization of the attracting fixed points which correspond to the roots of a polynomial. Also, numerical examples are included in order to show how to use the characterization of fixed points. Finally, we give a description of the parameter spaces of the methods under study applied to a one-parameter family of generic cubic polynomials. [ABSTRACT FROM AUTHOR]

In this paper we construct a class of Markov type operators which preserve e j , j ⩾ 1 . We give a recurrence relation for the moments of this operator and study the convergence. We show the uniform convergence of the derivative of order r ⩾ 0 of the operator. A Voronovskaya formula and some inequalities are presented. [ABSTRACT FROM AUTHOR]

In this paper, we derive discrete inequalities of the majorization type for convex functions by using Chebyshev type inequalities for synchronous sequences (cf. Otachel, 2011). Thus, some of the related results from Dragomir (2004) and Niezgoda (2008) are unified and extended. Applications for particular convex functions are given. [ABSTRACT FROM AUTHOR]

The paper deals with an effective implementation of some algorithms for the solution of convex QPQC problems with elliptic and other separable constraints with strong curvature. Here we discuss robust quantitative refinement of the Karush–Kuhn–Tucker conditions, extend existing results on the decrease of the cost function along the projected gradient path to separable constraints with elliptic components, and plug them into the existing algorithms for the solution of the QPQC problems with R-linear rate of convergence in the bounds on the spectrum. The results are then extended to the problems with separable inequality and linear equality constraints. The performance of the algorithms is demonstrated on the solution of a problem of two cantilever beams in mutual contact with orthotropic Tresca and Coulomb friction discretized by up to one and half million nodal variables. [ABSTRACT FROM AUTHOR]

Recently there has been renewed interest in the problem of finding under and over estimations on the set of convex functions to a given non-negative linear functional; that is, approximations which estimate always below (or above) the functional over a family of convex functions. The most important example of such an approximation problem is given by the multidimensional versions of the midpoint (rectangle) rule and the trapezoidal rule, which provide under and over estimations to the true value of the integral on the set of convex functions (also known as the Hermite–Hadamard inequality). In this paper, we introduce a general method of constructing new families of under/over-estimators on the set of convex functions for a general class of linear functionals. In particular, under the regularity condition, namely the functions belonging to C 2 ( Ω ) (not necessarily convex), we will show that the error estimations based on such estimators are always controlled by the error associated with using the quadratic function. The result is also extended to the class of Lipschitz functions. We also propose a modified approximation technique to derive a general class of under/over estimators with better error estimates. [ABSTRACT FROM AUTHOR]

The aim of this paper is to find a convenient and practical method to approximate a given real-valued function of multiple variables by linear operators, which approximate all strongly convex functions from above (or from below). Our main contribution is to use this additional knowledge to derive sharp error estimates for continuously differentiable functions with Lipschitz continuous gradients. More precisely, we show that the error estimates based on such operators are always controlled by the Lipschitz constants of the gradients, the convexity parameter of the strong convexity and the error associated with using the quadratic function, see Theorems 3.1 and 3.3. Moreover, assuming the function, we want to approximate, is also strongly convex, we establish sharp upper as well as lower refined bounds for the error estimates, see Corollaries 3.2 and 3.4. As an application, we define and study a class of linear operators on an arbitrary polytope, which approximate strongly convex functions from above. Finally, we present a numerical example illustrating the proposed method. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some integral inequalities of Hermite–Hadamard type involving the product of an s -convex function and a symmetric function and apply these new established inequalities to construct inequalities for special means. [ABSTRACT FROM AUTHOR]

In this paper, the authors establish some new estimates for the remainder term of the midpoint, trapezoid, and Simpson formula using functions whose derivatives in absolute value at certain power are s -convex. Some applications to special means of real numbers are provided as well. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new hybrid conjugate gradient method for solving unconstrained optimization problems. The proposed method can be viewed as a convex combination of Liu–Storey method and Dai–Yuan method. An remarkable property is that the search direction of this method not only satisfies the famous D–L conjugacy condition, but also accords with the Newton direction with suitable condition. Furthermore, this property is not dependent on any line searches. Under the strong Wolfe line searches, the global convergence of the proposed method is established. Preliminary numerical results also show that our method is robust and effective. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the complete monotonicities regarding both the functions σ x and λ x defined by Γ ( x + 1 ) = 2 π x x e x e σ x 12 x = 2 π x x e x ( 1 + λ x ) . As direct consequences, σ x is strictly increasing and strictly concave on ( 0 , ∞ ) and λ x is strictly decreasing and strictly convex on ( 0 , ∞ ) . Furthermore, we show that σ x consists the properties lim x → 0 + σ x = 0 and lim x → ∞ σ x = 1 as well as λ x holds the properties lim x → 0 + λ x = ∞ and lim x → ∞ λ x = 0 . [ABSTRACT FROM AUTHOR]

In this paper, we compare normalized Jensen functionals of two given convex functions defined on an interval of the real line. As applications, we give some valuable upper and lower bounds for the AGM inequality, which lead to some comparison results regarding Kullback–Leibler divergence and Shannon’s entropy. Some applications in inner product spaces are also included. [ABSTRACT FROM AUTHOR]

Univariate symmetrization technique has many good properties. In this paper, we adopt the high-dimensional viewpoint, and propose a new symmetrization procedure in arbitrary (convex) polytopes of ℝd with central symmetry. Moreover, the obtained results are used to extend to the arbitrary centrally symmetric polytopes the well-known Hermite-Hadamard inequality for convex functions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we establish convergence theorems for a general algorithm of an asymptotically nonexpansive map in a uniformly convex hyperbolic space. Our results generalize simultaneously the approximation results of Rhoades (1994) [18], Suantai (2005) [20] and Xu and Noor (2002) [26] on a nonlinear domain. Our results are refinements and generalizations of the corresponding ones in uniformly convex Banach spaces and spaces. [Copyright &y& Elsevier]

Abstract: In this paper, we study the set of cell matrices and its relationship with the cone of positive semidefinite diagonal matrices. The set forms a convex polyhedral cone in the linear space of symmetric matrices. We describe the faces of the cone and its polar. We also provide a new linear inequality associated with cell matrices. [Copyright &y& Elsevier]

Abstract: In this paper, the authors established Hermite–Hadamard’s inequalities for harmonically convex functions via fractional integrals and obtained some Hermite–Hadamard type inequalities of these classes of functions. [Copyright &y& Elsevier]

Abstract: In this paper, Hermite–Hadamard type inequality for Sugeno integrals based on -convex function is studied. Some examples are given to illustrate the results. [Copyright &y& Elsevier]

Abstract: In this paper we will point out a similar inequality to Hadamard’s for h-convex function defined on a disk. Some mappings connected with this inequality and related results are also obtained. [Copyright &y& Elsevier]

Abstract: In this paper we introduce the class of h-preinvex functions, and we prove some new inequalities for differentiable functions based on h-preinvexity. [Copyright &y& Elsevier]

Abstract: In this paper, we study harmonic mappings by using the shear construction, introduced by Clunie and Sheil-Small in 1984. We consider two classes of conformal mappings, each of which maps the unit disk univalently onto a domain which is convex in the horizontal direction, and shear these mappings with suitable dilatations . Mappings of the first class map the unit disk onto four-slit domains and mappings of the second class take onto regular n-gons. In addition, we discuss the minimal surfaces associated with such harmonic mappings. Furthermore, illustrations of mappings and associated minimal surfaces are given by using Mathematica. [Copyright &y& Elsevier]

Abstract: In this paper, we first establish sufficient conditions for the local uniqueness and Hölder continuity of perturbed solution set for a scalar optimization problem. Then, by using a linear scalarization method, we obtain the Hölder continuity of two classes of perturbed solution sets for a multiobjective programming problem, respectively. We also give some examples to illustrate that our main results are applicable. These examples are also given to illustrate that our main results are new and different from the ones in literature. [Copyright &y& Elsevier]

Abstract: By making use of the principle of differential subordination and the Dziok–Srivastava convolution operator, we introduce and investigate three interesting subclasses of analytic and univalent functions in the open unit disk. We obtain their inclusion relationships and also show that these classes are closed under convolution with convex functions. The results presented in this paper provide generalizations of several recent works by (for example) Özkan and Altıntaş (2006) [16], Trojnar-Spelina (2008) [30], and many other authors. [Copyright &y& Elsevier]

Abstract: This paper examines an optimal portfolio selection problem with a drawndown constraint based on mean–variance model when: (1) there is no arbitrage; (2) the market is complete; (3) there are finitely many states. First, we obtain the necessary and sufficient condition for the existence of the optimal solution to the problem. Then we prove that the efficient frontier of the model is a continuous and convex function, and the efficient frontier consists of a finite number of hyperbola segments and straight line segments with at most one subinterval corresponding to straight line segments. Moreover, we give some investment strategies by the results we obtained. Finally, we provide a numerical example to illustrate our results. [Copyright &y& Elsevier]

• The parameterized Douglas–Rachford splitting algorithm provides great flexibility for practical applications. We established the global convergence of PDR splitting method in a nonconvex setting. Moreover, we provide a convergence analysis for an adaptive DR algorithm in nonconvex settings as a byproduct. • Numerical experiments on nonconvex optimization problems such as sparse signal recovery nonconvex set feasibility problems and low rank matrix completion show the superiority compared to the other methods. In this paper, we study a parameterized Douglas–Rachford splitting method in Wang-Wang (2019)[5] for a class of nonconvex optimization problem. A new merit function is constructed to establish the convergence of the whole sequence generated by the parameterized Douglas–Rachford splitting method. As a by-product, this also provides convergence results of a special case of the adaptive Douglas–Rachford algorithm proposed by Dao and Phan (2019)[22] in nonconvex settings. We then apply the parameterized Douglas–Rachford splitting method to three important classes of nonconvex optimization problems arising in data science: sparsity constrained least squares problem, feasibility problem and low rank matrix completion. Numerical results validate the effectiveness of the parameterized Douglas–Rachford splitting method compared with some other classical methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper generalisations of Steffensen’s inequality obtained by Pečarić, Mercer and Wu–Srivastava are related. Some of this generalisations are showed to be equivalent and using Wu–Srivastava refinement of Steffensen’s inequality refined versions of Pečarić and Mercer’s results are obtained. Using Wu–Srivastava sharpened and generalized version of Mercer’s result sharpened version of generalization given by Pečarić is obtained. Furthermore, weaker conditions for some generalisations and refinements are obtained. Moreover, functionals defined as the difference between the left-hand and the right-hand side of generalizations and refinements of Steffensen’s inequality are studied. New Stolarsky type means, using several families of exponentially convex functions, related to defined functionals are generated. [Copyright &y& Elsevier]

Abstract: In the present paper, we introduce and investigate a certain new subclass of meromorphic close-to-convex functions. Such results as inclusion relationships, coefficient inequalities and convolution property are derived. Relevant connections of the results presented here with those obtained in earlier works are also pointed out. [Copyright &y& Elsevier]

Abstract: Let denote the class of analytic functions in the unit disc on the complex plane . If the operator satisfiesfor all , then it is called subordination-preserving operator on the class . In this paper we present a new result of this form which generalize some of the earlier and is connected with the Wilf’s conjecture. The applications of main result are also presented. [Copyright &y& Elsevier]