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In this paper, by using Poisson distribution probability, some characteristics of analytic multivalent q -symmetric starlike and q -symmetric convex functions of order η are examined. Then, by utilizing the Poisson distribution and the concept of the q -analogue Salagean integral operator, the p -valent convergence polynomial was introduced. Furthermore, a number of subclasses of analytic symmetric p -valent functions linked to novel polynomials are also deduced. After that, specific coefficient constraints are determined and symmetric δ , q -neighborhoods for p -valent functions are defined. In relation to symmetric δ , q -neighborhoods of q -symmetric p -valent functions formed by Poisson distributions, this paper presents new inclusion results. In addition, a detailed discussion of certain q -symmetric inequalities of analytic functions with negative coefficients is also provided. [ABSTRACT FROM AUTHOR]

In this paper, we employ a q -Noor integral operator to perform a q -analogue of certain fractional integral operator defined on an open unit disc. Then, we make use of the Hadamard convolution product to discuss several related results. Also, we derive a class of convex functions by utilizing the q -fractional integral operator and apply the inspired presented theory of the differential subordination, to geometrically explore the most popular differential subordination properties of the aforementioned operator. In addition, we discuss an exciting inclusion for the given convex class of functions. Over and above, we investigate the q -fractional integral operator and obtain some applications for the differential subordination. [ABSTRACT FROM AUTHOR]

In this paper, we give a characterization of Fredholmness of the Toeplitz operators on the Bergman spaces A φ p with exponential weights in D when 0 < p < ∞. Also, we obtain the sufficient and necessary conditions which the Toeplitz and Hankel operators on A φ 2 belong to h -Schatten class, where h is a continuous increasing convex function. [ABSTRACT FROM AUTHOR]

The study of convex functions is an interesting area of research due to its huge applications in pure and applied mathematics special in optimization theory. The aim of this paper is to introduce and study a more generalized class of convex functions. We established Schur (S), Hermite-Hadamard (HH), and Fejér (F) type inequalities for introduced class of convex functions. The results presented in this paper extend and generalize many existing results of the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study a generalized version of strongly reciprocally convex functions of higher order. Firstly, we prove some basic properties for addition, scalar multiplication, and composition of functions. Secondly, we establish Hermite-Hadamard and Fejér type inequalities for the generalized version of strongly reciprocally convex functions of higher order. We also include some fractional integral inequalities concerning with this class of functions. Our results have applications in optimization theory and can be considered extension/generalization of many existing results. [ABSTRACT FROM AUTHOR]

The fractional integral inequalities are crucial to deal applied problems. The present paper deals with the generalize midpoint type inequalities for a certain class of convex functions, namely, MT-convex functions in the setting of weighted fractional integral. It can be observed from the remarks given in the paper that our results or more generalized than existing results of literature and many of them can be obtained immediately from our results. [ABSTRACT FROM AUTHOR]

This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of the obtained identities, we present new trapezoid-type and midpoint-type inequalities via convex functions in the context of the conformable fractional integrals. New inequalities are obtained by taking advantage of the convexity property, power mean inequality, and Hölder's inequality. We show that this new family of inequalities generalizes some previous research studies by special choices. Furthermore, new other relevant results with trapezoid-type and midpoint-type inequalities are obtained. [ABSTRACT FROM AUTHOR]

In 2003, Mercer presented an interesting variation of Jensen's inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard inequalities of the Jensen–Mercer type via fractional integrals. As a result, we introduce several related fractional inequalities connected with the right and left differences of obtained new inequalities for differentiable harmonically convex mappings. As an application viewpoint, new estimates regarding hypergeometric functions and special means of real numbers are exemplified to determine the pertinence and validity of the suggested scheme. Our results presented here provide extensions of others given in the literature. The results proved in this paper may stimulate further research in this fascinating area. [ABSTRACT FROM AUTHOR]

In this paper, we give a generalized definition namely strongly α , h ‐ m -convex function that unifies many known definitions. By applying this new definition, we present inequalities for unified integral operators which have connection with many of the well-known results for different kinds of convex functions. Moreover, this paper at once provides refinements and generalizations of a lot of fractional integral inequalities which are identified in remarks. [ABSTRACT FROM AUTHOR]

This paper studies the distributed federated learning problem when the exchanged information between the server and the workers is quantized. A novel quantized federated averaging algorithm is developed by applying stochastic quantization scheme to the local and global model parameters. Specifically, the server broadcasts the quantized global model parameter to the workers; the workers update local model parameters using their own data sets and upload the quantized version to the server; then the server updates the global model parameter by aggregating all the quantized local model parameters and its previous global model parameter. This algorithm can be interpreted as a quantized variant of the federated averaging algorithm. The convergence is analyzed theoretically for both convex and strongly convex loss functions with Lipschitz gradient. Extensive experiments using realistic data are provided to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Let C and Q be closed convex subsets of real Hilbert spaces H1 and H2, respectively, and let g:C→R be a strictly real-valued convex function such that the gradient ∇g is an 1/L-ism with a constant L>0. In this paper, we introduce an iterative scheme using the gradient projection method, based on Mann’s type approximation scheme for solving the constrained convex minimization problem (CCMP), that is, to find a minimizer q∈C of the function g over set C. As an application, it has been shown that the problem (CCMP) reduces to the split feasibility problem (SFP) which is to find q∈C such that Aq∈Q where A:H1→H2 is a linear bounded operator. We suggest and analyze this iterative scheme under some appropriate conditions imposed on the parameters such that another strong convergence theorems for the CCMP and the SFP are obtained. The results presented in this paper improve and extend the main results of Tian and Zhang (2017) and many others. The data availability for the proposed SFP is shown and the example of this problem is also shown through numerical results. [ABSTRACT FROM AUTHOR]

The rapidly exploding of user data, especially applications of neural networks, involves analyzing data collected from individuals, which brings convenience to life. Meanwhile, privacy leakage in the applications as a potential threat needs to be addressed urgently. However, removing private information from models is difficult once the user's sensitive data enters machine learning models, particularly neural networks. Most of the previous amnestic methods based on retraining require full access to the training set of the target model and have limited improvements in computational resources and time improvement. In this paper, we propose Scrubber, which removes sensitive data from the original model via influence estimation to produce an unlearning model that is approximately indistinguishable from the retrained model. S crubber builds on the essential concept of influence function and reformulates the influence estimation as a closed‐form update of forgetting. For learned models with strictly convex loss functions, our approach theoretically guarantees the effectiveness of forgetting while empirically demonstrating forgetting performance. For models with non‐convex losses, we relax strictly convex assumptions by applying a damping term that allows us to make approximate estimates with negligible errors from the original assumption. Furthermore, experiments show that S crubber only causes less than 1% and 3% accuracy drop with more than 80% forgetting rate on average for logistic regression models and convolutional neural networks. The accuracy drop is reduced by 2%–3% compared to most state‐of‐the‐art methods. [ABSTRACT FROM AUTHOR]

In the present paper, q -fractional integral operators are used to construct quantum analogue of Ostrowski type inequalities for the class of s -convex functions. The limiting cases include the nonfractional existing cases from literature. Specially, Ostrowski type inequalities for q -integrals and Ostrowski type inequalities for convex functions are deduced. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new Newton's type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several new and existing inequalities for different fractional integrals like Riemann-Liouville fractional integrals, k -fractional integrals, Katugampola fractional operators, conformable fractional operators, Hadamard fractional operators, and fractional operators with the exponential kernel without proving one by one. It is also shown that the newly established inequalities are the refinements of the previously established inequalities inside the literature. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to give refinement of bounds of fractional integral operators involving extended generalized Mittag-Leffler functions. A new definition, namely, strongly α , m -convex function is introduced to obtain improvements of bounds of fractional integral operators for convex, m -convex, and α , m -convex functions. The results of this paper will provide simultaneous generalizations as well as refinements of various published results. [ABSTRACT FROM AUTHOR]

In this paper, the precoders capable of maximizing the weighted sum rate (WSR) for multicell scenarios under power budget constraint conditions per cell were considered based on the MIMO system performance. This rate is strongly affected by intracellular interference, so we recommend using coordinated beam forming (CBF). If the number of user equipment provided per cell is small enough to the number of transmit antennas, simple linear beamformers, such as matched filter (MF), achieve higher performance rates. In general cases, two algorithms meet the best performance in terms of the total achievable rate; these are KG (Kim Giannakis) and WSMSE (Weighted Sum Minimum Squared Error) algorithms. In the KG method, the objective function of the sum rate is suggested to be divided into two functions, one function for the desired user rate and the other for the sum rate of the remaining users. In the WSMSE algorithm, maximizing the sum rate is solved by redefining it as the problem of minimizing the MSE (Mean Square Error) function. These functions are convex and nonconvex functions, respectively. In the proposed method, the WSMSEs were modified to reduce the complexity and calculations to provide optimal performance in beamforming. [ABSTRACT FROM AUTHOR]

In the present paper, we deal with some fractional integral inequalities for strongly reciprocally p , h -convex functions. We established fractional version of Hermite-Hadamard and Fejér type inequalities for strongly reciprocally p , h -convex functions. Our results extend and generalize many exiting results of literate. [ABSTRACT FROM AUTHOR]

The aim of this paper is to derive from an auxiliary identity some new generalizations of fractional integral inequalities of Simpson, midpoint, and trapezoid using the class of harmonic convex functions. To show that our results are quite unifying, we discuss several new special cases. Finally, some applications regarding error estimations for the Simpson quadrature formula are presented to support our theoretical results. [ABSTRACT FROM AUTHOR]

This paper explores a designer-optimal reimbursement scheme in all-pay auctions with winner's reimbursement. Assuming the reimbursement is a linear function of the cost of effort, we obtain analytical solutions for the contestants' symmetrical equilibrium effort and the contest organizer's expected revenue. We show that if the effort cost function is concave, the optimal reimbursement scheme is to return the full cost to the winner. On the contrary, if the effort cost function is convex, the optimal reimbursement scheme is not to compensate the winner. Moreover, we find that the organizer's expected revenue may increase or decrease as the number of contestants increases when the winner is fully reimbursed. [ABSTRACT FROM AUTHOR]

In this paper, we concern with the split feasibility problem (SFP) whenever the convex sets involved are composed of level sets. By applying Gradient-projection algorithm which is used to solve constrained convex minimization problem of a real valued convex function, we construct two new algorithms for the split feasibility problem and prove that both of them are convergent weakly to a solution of the feasibility problem. In the end, as an application, we obtain a new algorithm for solving the split equality problem. [ABSTRACT FROM AUTHOR]

The new outcomes of the present paper are q -analogues (q stands for quantum calculus) of Hermite-Hadamard type inequality, Montgomery identity, and Ostrowski type inequalities for s -convex mappings. Some new bounds of Ostrowski type functionals are obtained by using Hölder, Minkowski, and power mean inequalities via quantum calculus. Special cases of new results include existing results from the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of uniform harmonic χ -convex functions. We show that this class relates several other unrelated classes of uniform harmonic convex functions. We derive a new version of Hermite-Hadamard's inequality and its fractional analogue. We also derive a new fractional integral identity using Caputo-Fabrizio fractional integrals. Utilizing this integral identity as an auxiliary result, we obtain new fractional Dragomir-Agarwal type of inequalities involving differentiable uniform harmonic χ -convex functions. We discuss numerous new special cases which show that our results are quite unifying. Finally, in order to show the significance of the main results, we discuss some applications to means of positive real numbers. [ABSTRACT FROM AUTHOR]

In this study, firstly we introduce a new concept called "strongly r-convex function." After that we establish Hermite-Hadamard-like inequalities for this class of functions. Moreover, by using an integral identity together with some well known integral inequalities, we establish several new inequalities for n-times differentiable strongly r-convex functions. In special cases, the results obtained coincide with the well-known results in the literature. [ABSTRACT FROM AUTHOR]

This paper proposes a nonconvex model (called LogTVSCAD) for deblurring images with impulsive noises, using the log-function penalty as the regularizer and adopting the smoothly clipped absolute deviation (SCAD) function as the data-fitting term. The proposed nonconvex model can effectively overcome the poor performance of the classical TVL1 model for high-level impulsive noise. A difference of convex functions algorithm (DCA) is proposed to solve the nonconvex model. For the model subproblem, we consider the alternating direction method of multipliers (ADMM) algorithm to solve it. The global convergence is discussed based on Kurdyka–Lojasiewicz. Experimental results show the advantages of the proposed nonconvex model over existing models. [ABSTRACT FROM AUTHOR]

In this paper, we define a strongly exponentially α , h − m -convex function that generates several kinds of strongly convex and convex functions. The left and right unified integral operators of these functions satisfy some integral inequalities which are directly related to many unified and fractional integral inequalities. From the results of this paper, one can obtain various fractional integral operator inequalities that already exist in the literature. [ABSTRACT FROM AUTHOR]

Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. In this paper, firstly we introduce the notion of h -exponential convex functions. This notion can be considered as generalizations of many existing definitions of convex functions. Then, we establish some well-known inequalities for the proposed notion via incomplete gamma functions. Precisely speaking, we established trapezoidal, midpoint, and He's inequalities for h -exponential and harmonically exponential convex functions via incomplete gamma functions. Moreover, we gave several remarks to prove that our results are more generalized than the existing results in the literature. [ABSTRACT FROM AUTHOR]

The rapid growth of video traffic poses serious challenges to the current Internet. Content-Centric Networking (CCN) as a promising candidate has been proposed to reengineer the Internet architecture. The in-network caching and named content communication model of CCN can enhance the video streaming applications and reduce the network workload. Due to the bandwidth-consuming characteristic of video streaming, the aggressive transmission of video data will cause a reduction of overall network efficiency. In this paper, we present an adaptive video transmission mechanism over Mobile Edge Computing- (MEC-) based CCN. The computation and storage resources of the MEC server are utilized to facilitate the video delivery. Our mechanism adopts a scalable video coding scheme to adaptively control transmission rate to cope with the network condition variation. To analyse the equilibrium property of the proposed mechanism, an analytical model is deduced by using network utility function and convex programming. We also take into account the packet loss in wired and wireless links and present a MEC assistant loss recovery algorithm. The experiment results demonstrate the performance improvement of our proposed mechanism. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to introduce I p , q ϱ -derivative and I p , q ϱ -integral for interval-valued functions and discuss their key properties. Also, we prove the I p , q ϱ -Hermite–Hadamard inequalities for interval-valued functions is the development of p , q ϱ -Hermite–Hadamard inequalities by using new defined I p , q ϱ -integral. Moreover, we prove some results for midpoint- and trapezoidal-type inequalities by using the concept of Pompeiu–Hausdorff distance between the intervals. It is also shown that the results presented in this paper are extensions of some of the results already shown in earlier works. The proposed studies produce variants that would be useful for performing in-depth investigations on fractal theory, optimization, and research problems in different applied fields, such as computer science, quantum mechanics, and quantum physics. [ABSTRACT FROM AUTHOR]

It is well-known that the logarithmic coefficients play an important role in the development of the theory of univalent functions. If S denotes the class of functions f z = z + ∑ n = 2 ∞ a n z n analytic and univalent in the open unit disk U , then the logarithmic coefficients γ n f of the function f ∈ S are defined by log f z / z = 2 ∑ n = 1 ∞ γ n f z n . In the current paper, the bounds for the logarithmic coefficients γ n for some well-known classes like C 1 + α z for α ∈ 0 , 1 and C V hpl 1 / 2 were estimated. Further, conjectures for the logarithmic coefficients γ n for functions f belonging to these classes are stated. For example, it is forecasted that if the function f ∈ C 1 + α z , then the logarithmic coefficients of f satisfy the inequalities γ n ≤ α / 2 n n + 1 , n ∈ ℕ. Equality is attained for the function L α , n , that is, log L α , n z / z = 2 ∑ n = 1 ∞ γ n L α , n z n = α / n n + 1 z n + ⋯ , z ∈ U. [ABSTRACT FROM AUTHOR]

This paper further studies the WYL conjugate gradient (CG) formula with βkWYL≥0 and presents a three-term WYL CG algorithm, which has the sufficiently descent property without any conditions. The global convergence and the linear convergence are proved; moreover the n-step quadratic convergence with a restart strategy is established if the initial step length is appropriately chosen. Numerical experiments for large-scale problems including the normal unconstrained optimization problems and the engineer problems (Benchmark Problems) show that the new algorithm is competitive with the other similar CG algorithms. [ABSTRACT FROM AUTHOR]

The present paper deals with the concept of generalized fuzzy invex monotonocities and generalized weakly fuzzy invex functions are introduced. Some necessary conditions for weakly fuzzy invex monotonocities are presented. Moreover, the concept of fuzzy strong invex monotonocities and fuzzy strong invex functions are also discussed. To strengthen our definitions, we provide nontrivial examples of fuzzy invex monotonocities and weakly fuzzy invex functions. [ABSTRACT FROM AUTHOR]

In this paper, two versions of the Hadamard inequality are obtained by using Caputo fractional derivatives and strongly m -convex functions. The established results will provide refinements of well-known Caputo fractional derivative Hadamard inequalities for m -convex and convex functions. Also, error estimations of Caputo fractional derivative Hadamard inequalities are proved and show that these are better than error estimations already existing in literature. [ABSTRACT FROM AUTHOR]

In this article, we have established the Hadamard inequalities for strongly convex functions using generalized Riemann–Liouville fractional integrals. The findings of this paper provide refinements of some fractional integral inequalities. Furthermore, the error bounds of these inequalities are given by using two generalized integral identities. [ABSTRACT FROM AUTHOR]

In this paper, we study the properties of n -polynomial ζ -preinvex functions and establish some integral inequalities of Hermite-Hadamard type via this class of convex functions. Moreover, we discuss some special cases which provide a significant complement to the integral estimations of preinvex functions. Applications of the obtained results to the inequalities for special means are also considered. [ABSTRACT FROM AUTHOR]

In this paper, we study the convergence rate of the proximal difference of the convex algorithm for the problem with a strong convex function and two convex functions. By making full use of the special structure of the difference of convex decomposition, we prove that the convergence rate of the proximal difference of the convex algorithm is linear, which is measured by the objective function value. [ABSTRACT FROM AUTHOR]

In this paper, the refinements of integral inequalities for all those types of convex functions are given which can be obtained from s , m -convex functions. These inequalities not only provide refinements of bounds for unified integral operators but also for various associated fractional integral operators containing Mittag–Leffler function. At the same time, presented results give generalizations of many known fractional integral inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we prove a general energy decay results of a coupled Lamé system with distributed time delay. By assuming a more general of relaxation functions and using some properties of convex functions, we establish the general energy decay results to the system by using an appropriate Lyapunov functional. [ABSTRACT FROM AUTHOR]

The purpose of the current paper is to investigate several various problems for the categories S T L s , S N e ∗ , and other related categories such as various new outcomes for the coefficients of f , together with majorization issues, the Hankel determinant, and the logarithmic coefficients with sharp inequalities and differential subordination implications. [ABSTRACT FROM AUTHOR]

In this paper, we propose a constellation amplitude modification (CAM) method to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing systems. The key idea of the proposed CAM method is to modify the original constellation amplitude and choose the constellation points with the minimum PAPR as the transmitted constellation points. The CAM method formulates the PAPR reduction as a convex optimization problem, and then, it applies the customized interior-point method to solve the optimization problem. Compared with the traditional methods, the CAM method does not increase the transmit power, and the receiver has no additional operations. Simulation results show that the CAM method converges fast and offers significant PAPR reduction. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the fractional Hadamard and Fejér-Hadamard inequalities for exponentially s , m -convex functions. To establish these inequalities, we will utilize generalized fractional integral operators containing the Mittag-Leffler function in their kernels via a monotone function. The presented results in particular contain a number of fractional Hadamard and Fejér-Hadamard inequalities for s -convex, m -convex, s , m -convex, exponentially convex, exponentially s -convex, and convex functions. [ABSTRACT FROM AUTHOR]

The field of stochastic processes is essentially a branch of probability theory, treating probabilistic models that evolve in time. It is best viewed as a branch of mathematics, starting with the axioms of probability and containing a rich and fascinating set of results following from those axioms. In probability theory, a convex function applied to the expected value of a random variable is always bounded above by the expected value of the convex function of the random variable. In this paper, the concept of generalized h -convex stochastic processes is introduced, and some basic properties concerning generalized h -convex stochastic processes are developed. Furthermore, we establish Jensen and Hermite–Hadamard and Fejér-type inequalities for this generalization. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two novel total variation models to deal with speckle noise in ultrasound image in order to retain the fine details more effectively and to improve the speed of energy diffusion during the process. Firstly, two new convex functions are introduced as regularization term in the adaptive total variation model, and then, the diffusion performances of Hypersurface Total Variation (HYPTV) model and Logarithmic Total Variation (LOGTV) model are analyzed mathematically through the physical characteristics of local coordinates. We have shown that the larger positive parameter in the model is set, the greater energy diffusion speed appears to be, but it will cause the image to be too smooth that required adequate attention. Numerical experimental results show that our proposed LOGTV model for speckle noise removal is superior to traditional models, not only in visual effect but also in quantitative measures. [ABSTRACT FROM AUTHOR]

Some basic properties in Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F -norm are studied in this paper. We give some relationships between the modulus and the Mazur-Orlicz F -norm. We obtain an interesting result that the norm of an element in line segments is formed by two elements on the unit sphere less than or equal to 1 if and only if that the monotone function is a convex function. The criterion that Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F -norm are strictly monotone or lower locally uniform monotone is presented. [ABSTRACT FROM AUTHOR]

This paper deals with the global existence of solutions in a bounded domain for nonlinear viscoelastic Kirchhoff system with a time varying delay by using the energy and Faedo–Galerkin method with respect to the delay term weight condition in the feedback and the delay speed. Furthermore, by using some convex functions properties, we prove a uniform stability estimate. [ABSTRACT FROM AUTHOR]

This paper established some new Hermite–Hadamard type inequalities for ψ -Riemann–Liouville fractional integrals via convex functions. As applications, we applied the inequalities to special means of real numbers and constructed inequalities for the beta function. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear viscoelastic Kirchhoff equation in a bounded domain with a time-varying delay term and logarithmic nonlinearity in the weakly nonlinear internal feedback is considered, where the global and local existence of solutions in suitable Sobolev spaces by means of the energy method combined with Faedo-Galerkin procedure is proved with respect to the condition of the weight of the delay term in the feedback and the weight of the term without delay and the speed of delay. Furthermore, a general stability estimate using some properties of convex functions is given. These results extend and improve many results in the literature. [ABSTRACT FROM AUTHOR]

This paper is concerned with a nonlinear viscoelastic Kirchhoff plate u t t t − σ Δ u t t t + Δ 2 u t − ∫ 0 t g t − s Δ 2 u s d s = div F ∇ u t . By assuming the minimal conditions on the relaxation function g : g ′ t ≤ ξ t G g t , where G is a convex function, we establish optimal explicit and general energy decay results to the system. Our result holds for G t = t p with the range p ∈ 1 , 2 , which improves earlier decay results with the range p ∈ 1 , 3 / 2 . At last, we give some numerical illustrations and related comparisons. [ABSTRACT FROM AUTHOR]

In the paper, the author introduces a new class of harmonically convex functions, which is called harmonically α,s-convex functions and establishes some new integral inequalities of the Hermite-Hadamard type for harmonically α,s-convex functions. The properties of the newly introduced class of harmonically convex functions are also investigated. Finally, some applications to special means are given. [ABSTRACT FROM AUTHOR]

This paper considers problems of economic dispatch in power networks that contain independent power generation units and loads. For efficient distributed economic dispatch, we present a mechanism of multiagent learning in which each agent corresponding to a generation unit updates the power generation based on the received information from the neighborhood. The convergence of the proposed distributed learning algorithm to the global optimal solution is analyzed. Another method of distributed economic dispatch we propose is a decentralized iterative linear projection method in which the necessary optimality conditions are solved without considering the generation capacities and the obtained solutions are iteratively projected onto the convex set corresponding to the generation capacities. A centralized method based on semidefinite programming for economic dispatch with a loss coefficient matrix is also presented for comparisons. For demonstration, the proposed methods of distributed economic dispatch are applied to a 6-generator test case and the three different methods of economic dispatch give the same solutions. We also analyze parametric dependence of the optimal power generation profiles on varying power demands in economic dispatch. [ABSTRACT FROM AUTHOR]

Total variation image denoising models have received considerable attention in the last two decades. To solve constrained total variation image denoising problems, we utilize the computation of a resolvent operator, which consists of a maximal monotone operator and a composite operator. More precisely, the composite operator consists of a maximal monotone operator and a bounded linear operator. Based on recent work, in this paper we propose a fixed-point approach for computing this resolvent operator. Under mild conditions on the iterative parameters, we prove strong convergence of the iterative sequence, which is based on the classical Krasnoselskii–Mann algorithm in general Hilbert spaces. As a direct application, we obtain an effective iterative algorithm for solving the proximity operator of the sum of two convex functions, one of which is the composition of a convex function with a linear transformation. Numerical experiments on image denoising are presented to illustrate the efficiency and effectiveness of the proposed iterative algorithm. In particular, we report the numerical results for the proposed algorithm with different step sizes and relaxation parameters. [ABSTRACT FROM AUTHOR]