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• Double bias fields are introduced into fidelity term to approximate image intensity inhomogeneity. • The proposed energy function is strictly convex, and allows flexible initialization. • A TV (total variation) regularization term is introduced to keep convex level-set function smooth. • The proposed method is robust against to noise and intensity inhomogeneity. The existing active contour models (ACMs) based on bias field (BF) correction mostly rely on a single BF assumption and lack in-depth discussion on the convexity of the energy functional, often leading to the problem of local minima. To address this issue, this paper introduces a dual BF and proposes a convex level-set (LS) method based on multiplicative-additive (MA) model to achieve global minima. Firstly, a MA model is adopted as the fidelity term, and a kernel function is introduced to adjust the size of the intensity inhomogeneous neighborhood, enhancing the adaptability to intensity inhomogeneity. Then, the convex LS function is embedded in the variational framework to ensure convexity of each variable in the energy functional. This transformation turns the segmentation problem into a convex optimization problem. By introducing the total variation regularization term to smooth the LS function, the model's resistance to noise is effectively enhanced. Finally, by minimizing the proposed energy functional, image segmentation and BF correction are successfully achieved. Experimental results validate the global minima property of our model, while also demonstrating good flexibility in the initial contour. The proposed model achieves superior segmentation results compared to other classical ACMs on various types of images. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of nonconvex and nonsmooth fractional optimization problem, where the numerator of which is the sum of a nonsmooth and nonconvex function and a relative smooth nonconvex function, while the denominator is relative weakly convex nonsmooth function. We propose a Bregman proximal subgradient algorithm for solving this type of fractional optimization problems. Under moderate conditions, we prove that the subsequence generated by the proposed algorithm converges to a critical point, and the generated sequence globally converges to a critical point when the objective function satisfies the Kurdyka-Łojasiewicz property. We also obtain the convergence rate of the proposed algorithm. Finally, two numerical experiments illustrate the effectiveness and superiority of the algorithm. Our results give a positive answer to an open problem proposed by Bot et al. [14]. [ABSTRACT FROM AUTHOR]

In this paper, a novel non-convex fractional-order image denoising model is proposed to suppress the staircase effect produced by the TV model while maintaining a neat contour. The model combines ℓ q (0 < q < 1) quasi-norm and fractional-order regularization, and employs a diffusion coefficient with a faster convergence rate to preserve more image edges and details. Additionally, an adaptive regularization parameter is designed to adjust the denoising performance of the algorithm. To obtain the optimal approximate solution of the model, an enhanced primal-dual algorithm is adopted and the complexity and convergence of the algorithm are theoretically analyzed. Finally, the effectiveness of the proposed method is demonstrated through numerical experiments. • A new non-convex FOTV model is proposed. • A new diffusion coefficient is introduced to retain more edge details of the image. • The existing primal-dual algorithm is improved, and the convergence of this algorithm is analyzed. • An adaptive regularization parameter is designed. [ABSTRACT FROM AUTHOR]

The general first Zagreb index of a graph G , denoted by M 1 p (G) , is defined as the sum of powers d G p (u) over all vertices u of V (G) , where d G (u) denotes the degree of a vertex u in G. In this paper, we consider negative values of p and obtain sharp lower bounds on the general first Zagreb index of trees, unicyclic and bicyclic graphs in terms of their order and maximum vertex degrees. Also, the corresponding extremal graphs attaining the bounds are characterized. The results are then extended to other indices defined as sums over all vertices of contributions which are convex or concave functions of their degrees. [ABSTRACT FROM AUTHOR]

This paper is devoted to the stability analysis of a class of discrete-time switched systems under newly designed switching regularities. The utilized switching is extended from the primitive mode-dependent persistent dwell-time switching. By integrating the existing admissible edge-dependent average dwell-time switching into the mode-dependent persistent dwell-time regime, a novel admissible edge-dependent average persistent dwell-time strategy involving the notion of admissible transition edges is proposed. The integrated admissible edge-dependent average dwell-time switching has been confirmed to be superior to mode-dependent average dwell-time switching. This superiority makes the proposed switching more general than the relaxed mode-dependent persistent dwell-time switching in the literature. Even if the embedded admissible edge-dependent average dwell-time restrictions degrade to admissible edge-dependent dwell-time ones under special parameter settings, the resulting admissible edge-dependent persistent dwell-time switching retains the advantage of admissible transition edges to generalize the original mode-dependent persistent dwell-time switching. Meanwhile, to remove the switching information reliance in the existing multiple convex Lyapunov functions, an improved multiple convex Lyapunov function method is devised. The designed Lyapunov function can be used to implement broader feasible ranges and tighter lower bounds of admissible edge-dependent average persistent dwell-time (or admissible edge-dependent persistent dwell-time). Finally, the validity and efficiency of the presented approaches are illustrated by a three-phase inverter and a numerical example. • Admissible edge-dependent average persistent dwell-time switching is proposed. • Admissible edge-dependent persistent dwell-time switching is proposed. • A more widely applicable multiple convex Lyapunov function is raised. [ABSTRACT FROM AUTHOR]

The concept of jump system, introduced by Bouchet and Cunningham (1995), is a set of integer points satisfying a certain exchange property. We consider the minimization of a separable convex function on a jump system. It is known that the problem can be solved by a greedy algorithm. In this paper, we are interested in whether the greedy algorithm has the geodesic property, which means that the trajectory of the solutions generated by the algorithm is a geodesic from the initial solution to a nearest optimal solution. We show that a special implementation of the greedy algorithm enjoys the geodesic property, while the original algorithm does not. As a corollary to this, we present a new greedy algorithm for linear optimization on a delta-matroid and show that the algorithm has the geodesic property. [ABSTRACT FROM AUTHOR]

For a graph G = (V G , E G) , a subset S ⊆ V G is called a maximum dissociation set if the induced subgraph G [ S ] does not contain P 3 as its subgraph, and the subset has maximum cardinality. The dissociation number of G is the number of vertices in a maximum dissociation set of G. This paper mainly studies the problem of determining the maximum values of the vertex-degree function index H f (G) = ∑ v ∈ V G f (d (v)) and characterizing the corresponding extremal graphs among all trees and unicyclic graphs with fixed order and dissociation number when f (x) is a strictly convex function. Firstly, we describe all the trees having the maximum vertex-degree function index H f (T) among trees with given order and dissociation number when f (x) is a strictly convex function. Then we determine the graphs having the maximum vertex-degree function index H f (T) among unicyclic graphs with given order and dissociation number when f (x) is a strictly convex function and satisfies f (5) + 2 f (3) + f (2) > 3 f (4) + f (1). [ABSTRACT FROM AUTHOR]

In many high-dimensional datasets, the phenomenon that features are relevant often occurs. Elastic-net regularization is widely used in support vector machines (SVMs) because it can automatically perform feature selection and encourage highly correlated features to be selected or removed together. Recently, some effective algorithms have been proposed to solve the elastic-net SVMs with different convex loss functions, such as hinge, squared hinge, huberized hinge, pinball and huberized pinball. In this paper, we develop a linearized alternating direction method of multipliers (LADMM) algorithm to solve above elastic-net SVMs. In addition, our algorithm can be applied to solve some new elastic-net SVMs such as elastic-net least squares SVM. Compared with some existing algorithms, our algorithm has comparable or better performances in terms of computational cost and accuracy. Under mild conditions, we prove the convergence and derive convergence rate of our algorithm. Furthermore, numerical experiments on synthetic and real datasets demonstrate the feasibility and validity of the proposed algorithm. • We develop a linearized ADMM algorithm for effectively solving a series of elastic-net SVMs. • The proposed algorithm is accompanied by convergence and complexity analysis. • A new elastic-net SVM called LESVM is proposed in this paper. [ABSTRACT FROM AUTHOR]

[Display omitted] • A model for multi-objective optimization operation of multiple water sources under uncertainties was proposed. • Uncertainties in inflow and water demand forecasts can be considered simultaneously, and the correlation between uncertainties can be considered quantitatively. • The impact of inflow-water demand forecast uncertainties and their correlations on water resource operations are explored for water resources managers. Uncertainties in inflow and water demand forecasts bring risks to water resources management. Therefore, the research on multi-objective optimization operation of multiple water sources under uncertainties holds critical research significance and application value. This paper proposes a model for the multi-objective optimization operation of multiple water sources that can consider the inflow and water demand forecast dual uncertainties. In handling uncertainties, this paper adopts a scenario generation method based on joint distribution-Monte Carlo (JDMC), which allows for a quantitative consideration of the correlation between uncertainties. Moreover, the variable weight method and LINGO 20.0 are employed for solving multi-objective optimization issues to obtain stable Pareto frontiers. The proposed model is applied to the water receiving area inside Jiangsu Province of the South-to-North Water Transfer East Route Project (SNWTERP) in China. The main findings are as follows: 1) The impact of the inflow and water demand forecast uncertainties on the operation results is synergistic rather than antagonistic. Considering only a single uncertainty may result in water receiving area facing more severe water shortages or purchasing spot water at high prices. 2) There is a strong spatial correlation between uncertainties. If we ignore or only qualitatively consider the correlation between uncertainties, the impact of uncertainties on operation results will be underestimated or overestimated. 3) The Pareto frontiers are convex functions, indicating that decision-makers should choose a solution in the middle part. [ABSTRACT FROM AUTHOR]

In this paper, we study the Differentially Private Empirical Risk Minimization (DP-ERM) problem, considering both convex and non-convex loss functions. For cases where DP-ERM involves smooth (strongly) convex loss functions with or without non-smooth regularization, we propose several novel methods. These methods achieve (near) optimal expected excess risks (i.e., utility bounds) while reducing the gradient complexity compared to existing approaches. When dealing with DP-ERM and smooth convex loss functions in high dimensions, we introduce an algorithm that achieves a superior upper bound with lower gradient complexity than previous solutions. In the second part of the paper, for DP-ERM with non-convex loss functions, we explore both low and high dimensional spaces. In the low dimensional case with a non-smooth regularizer, we extend an existing approach by measuring the utility using the ℓ 2 norm of the projected gradient. Furthermore, we introduce a novel error bound measurement, transitioning from empirical risk to population risk by employing the expected ℓ 2 norm of the gradient. For the high dimensional case, we demonstrate that by measuring utility with the Frank-Wolfe gap, we can bound the utility using the Gaussian Width of the constraint set, instead of the dimensionality (p) of the underlying space. We also show that the advantages of this approach can be achieved by measuring the ℓ 2 norm of the projected gradient. Finally, we reveal that the utility of certain special non-convex loss functions can be reduced to a level (depending only on log ⁡ p) similar to that of convex loss functions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate regularized online exponentially concave (abbr. exp-concave) optimization, in which each loss function consists of a time-varying exp-concave function and a fixed convex regularization. If the whole loss function is exp-concave, a classical method called online Newton step (ONS) enjoys an O (d log T) regret bound, where d is the dimensionality and T is the time horizon. However, in the regularized setting, the sum of an exp-concave function and a convex regularization is not necessarily an exp-concave function, which implies that ONS is not applicable. To address this problem, we propose the proximal online Newton step (ProxONS), and show that it can attain the same O (d log T) regret bound for any convex regularization. The main idea is to first perform an iteration of ONS with the exp-concave part in each loss function and then perform a proximal mapping with the regularization part. Furthermore, we demonstrate that by utilizing the standard online-to-batch conversion, our ProxONS can be extended to solve stochastic optimization with a regularized exp-concave objective, and enjoy an O (d log T / T) convergence rate with high probability. Experimental results on two real datasets verify the effectiveness of our ProxONS. [ABSTRACT FROM AUTHOR]

This paper presents two kinds of novel results about semiglobal synchronization in probability for stochastic systems. To this end, new criteria of semiglobal fixed-time synchronization in probability (SFXTSp) and semiglobal preassigned-time synchronization in probability (SPATSp) are proposed. In contrast to the existing results of semiglobal synchronization in probability, our criteria have wider applicability in SFXTSp and SPATSp due to their flexible forms. Meanwhile, based on the properties of convex functions and Jensen's inequality, our approaches overcome the issue arising from the non-equivalence between the Lyapunov function and its expectation, making our conclusions more rigorous. In addition, to achieve SFXTSp of stochastic neural networks with random delay (RDSNNs), a unified adaptive controller is developed. By modifying the parameters of the unified controller, RDSNNs reach SPATSp in a predetermined time. Ultimately, numerical simulations are conducted to confirm the practicality and accuracy of the derived outcomes. • Two novel semiglobal synchronization in probability results are proposed. • Our conclusions have wider applicability and address the existing challenges. • Various stochastic factors are considered, making our results more general. • Our unified controller is generalized to achieve two kinds of synchronization. [ABSTRACT FROM AUTHOR]

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]

The tensor completion(TC) problem has attracted wide attention due to its significant practical significance and broad application background. Various approaches have been used to solve this problem, including approximating the rank function through its convex envelope, the tensor nuclear norm. However, due to the gap between the rank function and its convex envelope, this approach often fails to achieve satisfactory recovery. Recent developments have highlighted that non-explicit non-convex functions, especially the one induced by the Smooth Hard(SH) shrinkage operator, can approximate the l 0 norm more effectively compared to other methods, and this function facilitates the reconstruction of noisy MRI data with minimal sampling rate requirements. In our paper, we implement the SH shrinkage operator within the TC framework, achieving accurate tensor data recovery at lower sampling rates. Moreover, we adopt a method that adaptively generates transformation matrices based on specific features of the data, which, compared to traditional TC models, can better exploit the inherent low-rank properties of tensor data. Additionally, our approach integrates a reweighting strategy to efficiently merge tensors recovered from various dimensions. Finally, a feasible minimization algorithm is proposed, which combines the non-explicit non-convex regularizer and self-adaptive transforms. It is proven that the constructed sequence of the proposed algorithm is a Cauchy sequence and can converge to a stable point. Extensive experimental results demonstrate that our proposed approach can achieve accurate tensor recovery at lower sampling rates compared to other methods. • We apply the SAT method to each dimension. • We combine the SH shrinkage operator with the SAT method. • we reweight the recovered tensors obtained from each dimension. [ABSTRACT FROM AUTHOR]

In recent years, a class of soft (deformable) robots has attracted the attention of researchers due to their continuum features being advantageous over rigid robots for dexterous and safe compliant motions. These distinct advantages are obtained from the elastomer hyperelastic material properties because continuum robots are manufactured and actuated through embedded pneumatic energy fields. In this way, the continuum deformation raises novel problems in modeling and control due to its highly nonlinear behavior. That is, the deformable shape of its components varies continuously, unlike rigid robots, suggesting that the controller should compensate for its varying continuum model. Motivated by the deformable soft robot subject to parametric uncertainties and unmodeled dynamics, this paper proposes an adaptive, instead of constant, tuning of feedback gains of a model-free controller. The tuning mechanism is based on a knowledge-based scheme using a discrete wavelet neural network (DWN) by an efficient input–output identification updating its parameters and weights online, with a gradient descent algorithm driven by the identification error. At the same time, the control feedback gains are self-tuned, minimizing a convex cost function of tracking errors. Dynamic simulations show the performance of the proposed approach considering the parameters of a real soft robot mimicking a gelatin-like behavior. Finally, some discussions on the proposed scheme's computational cost, feasibility, and viability are briefly addressed. [ABSTRACT FROM AUTHOR]

In this paper, we consider a secure full-duplex (FD) multi-user multiple-input multiple-output (MU-MIMO) network where an FD base station simultaneously communicates with users and transfers energy for untrusted energy harvesting (EH) devices. Considering that the EH users are untrusted and try to wiretap the signals, the base station adds artificial noise (AN) signals into its transmitted signals to enhance the system security. We focus on two single-objective optimization problems including (i) the sum secrecy rate maximization problem, (ii) the harvested energy maximization problem, and a multi-objective optimization problem of the secure information and EH trade-off. The goal is to jointly optimize the transmit covariance matrices of the precoding and AN jamming under the constraints on transmit power budgets, harvested energy requirements, and minimum secrecy rates. Three considered optimization problems are highly non-convex due to the non-convexity of the sum secrecy rate. To handle this challenge, we first recast the sum secrecy rate as the inner convex approximation one thanks to the difference of two convex functions (DC) approach. Then, the sequential convex programming (SCP) approach is utilized to iteratively find the optimal solution. The numerical simulations are provided to investigate the impacts of the system settings and residual self-interference on the achievable system performances in terms of the secrecy rate and harvested energy. Furthermore, the numerical results also reveal the interesting trade-offs between the secrecy rate and harvested energy. [ABSTRACT FROM AUTHOR]

In this paper, we establish a novel identity by leveraging fractional integral operators of Riemann-type. Subsequently, we employ this identity to investigate Bullen's fractional integral inequalities within the framework of classical convex functions. The validity of these innovative inequalities is verified through the visualization of 2D and 3D graphs. Furthermore, we obtain certain well-known results as special cases to our main findings and express them as remarks. Lastly, we derive differences in mean estimates, which serve as valuable tools for representing complex information, facilitating decision-making and aiding analysis in various fields. [ABSTRACT FROM AUTHOR]

In this paper, we present a multiplicative fractional integral identity. Based upon it, we establish the Hermite–Hadamard type inequalities for multiplicatively convex functions via multiplicative Riemann–Liouville fractional integrals. We also give some applications to special means of real numbers in the framework of multiplicative calculus. To make the results obtained here more intuitive for the readers, we provide some examples for suitable choices of multiplicative convex functions and their graphical descriptions. • A multiplicative fractional *integral identity is developed. • Fractional HH type inequalities for *differentiable functions are established. • Applications of the obtained results are considered as well. [ABSTRACT FROM AUTHOR]

This paper addresses the global optimal consensus problem with time-varying objective functions and state-coupled inequality constraints. By integrating the predefined-time consensus and prediction-correction schemes, a distributed optimization protocol is proposed for the cooperative interception scenarios involving the unmanned aerial vehicle (UAV) swarm. Specifically, the δ -exact penalty method is utilized to eliminate the coupled constraints. A prediction-correction term with the penalty function is then established to track the trajectory of the time-varying optimal solution. Additionally, an edge-based predefined-time consensus term is introduced to facilitate the state consensus among UAVs. Under the undirected and connected topology, the proposed protocol ensures the predefined-time state consensus and asymptotically minimizes the sum of individual convex objective functions. Furthermore, the protocol is extended to other scenarios involving switching topology, directed detail-balanced topology, and external disturbances. Numerical simulations illustrate that the UAV swarm can form the predesigned interception formation with a predefined-time frame and effectively track the target swarm. [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]

Combined heat and power economic dispatch (CHPED) can enhance energy efficiency compared with conventional economic dispatch (ED). From the optimization standpoint, the CHPED problem usually involves the nonlinear products of heat and power generation variables, nonconvex objective functions, and nonconvex feasible operating range. Thus, its solution method should be able to cope with the problematic nonconvex problem since finding a poor solution for the CHPED implies reducing the maximum achievable efficiency. This paper presents an effective method utilizing several mathematical transformations to cope with the nonlinear, nonconvex terms. The method transforms the nonconvex regions and nonlinear functions into convex polyhedrons and segments. Then, the method formulates the polyhedrons and segments with integer variables, logical constraints, and combinatorial restrictions. Thus, we derive a mixed integer model, which optimization software can better solve. Simulation results illustrate the effectiveness of the method presented and its advantages compared with existing CHPED solution techniques in the literature. [Display omitted] • Transforming nonconvex feasible operating ranges in CHP units into some polyhedrons. • Converting nonconvex cost functions into linear segments. • Presenting a robust solution method for the optimal operation of a CHP. [ABSTRACT FROM AUTHOR]

The topic of synchronization of fractional-order fuzzy complex networks with time-varying couplings and proportional delay is addressed in this paper. By combining graph theory, the Lyapunov method, and the Razumikhin method, the synchronization criteria are obtained by designing a new time-varying graph-theoretical Lyapunov function. Different from the typical quadratic Lyapunov function, the time-varying graph-theoretical Lyapunov function contains the product of three-term functions and poses the difficulty of fractional derivative due to the unavailability of the general Leibniz formula and the chain rule. A new inequality about the fractional derivative rule of the time-varying graph-theoretical Lyapunov function is established based on the convex function creatively. In addition, compared with relevant literatures, the synchronization criteria are related to the proportionality coefficient and the order of fractional derivative. Then, the synchronization of fractional-order power system established on fuzzy complex networks with time-varying couplings and proportional delay is studied for the first time by applying the feedback control. Lastly, some simulations are exhibited to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Let μ be a probability measure on R d with barycenter at the origin, which is supported on an open, bounded and convex set K having smooth boundary and positive Gauss curvature. Suppose that d μ x = ϱ x − α d x , with α > d + 1 and ϱ : K → 0 , + ∞ is C ∞ -smooth, satisfies ɛ 0 -convex condition for some ɛ 0 > 0 such that ϱ and its first derivatives are bounded in K. In this paper, we prove that for any convex solution ψ : R d → 0 , + ∞ to the following Monge–Ampère equation (1) [ ϱ ∇ ψ x ] − α det ( ∇ 2 ψ x ) = (ψ x ) − α , x ∈ R d the function x ↦ log ψ x has second derivatives to be bounded by a constant C ɛ 0 depending on ɛ 0 , α , ψ (x 0) and values of first, second and fourth derivatives of ψ at a fixed point x 0 ∈ R d . This estimate is as a variant case of the Caffarelli contraction theorem by replacing target densities of e − W by densities of ϱ − α that Cauchy distributions (i.e., ϱ x − α = 1 + | x | 2 − α ) are typical examples. [ABSTRACT FROM AUTHOR]

Recently, introducing nonconvex loss functions in support vector machine (SVM) to improve the robustness against varies noises has been drawing much attention. In this paper, we first construct a new robust capped asymmetric elastic net (CaEN) loss function. Second, we describe a novel robust Huberized kernel-based (HK) loss function and theoretically demonstrate several important properties, such as smoothness, boundness and the trade-off between the standard least squares and the truncated least squares. Finally, we apply the CaEN loss and the HK loss into elastic net nonparallel hyperplane SVM (ENNHSVM) to develop a fused robust geometric nonparallel SVM (FRGNHSVM). The proposed FRGNHSVM not only inherits the advantages of ENNHSVM but also improves the robustness of classification problems. An efficient Pegasos-based DC (difference of convex functions) algorithm is implemented to solve the FRGNHSVM optimization problem. In comparison with four famous SVMs, including Lagrangian SVM, twin SVM, pinball SVM and C-loss twin SVM, experimental results on simulations and twelve UCI datasets show that the proposed FRGNHSVM can often improve more than 5% average prediction accuracy. Moreover, the performance of the high prediction accuracy of FRGHNSVM is more significant along with the ratio of label noise increasing, indicating its superiority in dealing with label-contaminated datasets. • A novel FRGNHSVM is proposed for robust binary learning problems. • FRGNHSVM is stable for re-sampling and robust to outliers. • The designed Pegasos-based DC algorithm is scalable and applicable to large data. • Experimental results demonstrate the effectiveness of FRGNHSVM. [ABSTRACT FROM AUTHOR]

This paper introduces a novel state estimator designed for discrete-time nonlinear dynamical systems that encompass unknown-but-bounded uncertainties, along with state linear inequality and nonlinear equality constraints. Our algorithm is based on constrained zonotopes (CZs) and employs a DC programming approach (where DC stands for difference of convex functions). Recently, techniques such as mean value extension and first-order Taylor extension have been adapted from zonotopes to facilitate the propagation of CZs across nonlinear mappings. While the resulting algorithms, known as CZMV and CZFO, achieve higher precision compared to the original zonotopic versions, they still exhibit sensitivity to the wrapping and dependency effects inherent in interval arithmetic. These interval-related challenges can be mitigated through the use of DC programming, as it allows for the determination of approximation error bounds by solving optimization problems. One direct advantage of this technique is the elimination of the dependency effect. Our set-membership filter, referred to as CZDC, provides an alternative solution to CZMV and CZFO. To showcase the effectiveness of our proposed approach, we conducted experiments using CZDC on two numerical examples. [ABSTRACT FROM AUTHOR]