Second-order Constraints Research Articles

Measures of stochastic non-dominance in portfolio optimization

Stochastic dominance rules are well-characterized and widely used. This work aims to describe and better understand the situations when they do not hold by developing measures of stochastic non-dominance. They quantify the error caused by assuming that one random variable dominates another one when it does not. To calculate them, we search for a hypothetical random variable that satisfies the stochastic dominance relationship and is as close to the original one as possible. The Wasserstein distance between the optimal hypothetical random variable and the original one is considered as the measure of stochastic non-dominance. Depending on the conditions imposed on the probability distribution of the hypothetical random variable, we distinguish between general and specific measures of stochastic non-dominance. We derive their exact values for random variables with uniform, normal, and exponential distributions. We present relations to almost first-order stochastic dominance and to tractable almost stochastic dominance. Using monthly returns of twelve assets captured by the German stock index DAX, we solve portfolio optimization problems with the first-order and second-order stochastic dominance constraints. The measures of stochastic non-dominance allow us to compare the optimal portfolios with respect to different orders of stochastic dominance from a new angle. We also defined the closest dominating and closest approximately dominating portfolios. They brought a better understanding of the relationship between the two types of optimal portfolios. Using moving window analysis, the relationship of the in-sample measure of stochastic non-dominance to out-of-sample performance was studied, too.

HPRN: Holistic Prior-Embedded Relation Network for Spectral Super-Resolution.

Spectral super-resolution (SSR) refers to the hyperspectral image (HSI) recovery from an RGB counterpart. Due to the one-to-many nature of the SSR problem, a single RGB image can be reprojected to many HSIs. The key to tackle this ill-posed problem is to plug into multisource prior information such as the natural spatial context prior of RGB images, deep feature prior, or inherent statistical prior of HSIs so as to effectively alleviate the degree of ill-posedness. However, most current approaches only consider the general and limited priors in their customized convolutional neural networks (CNNs), which leads to the inability to guarantee the confidence and fidelity of reconstructed spectra. In this article, we propose a novel holistic prior-embedded relation network (HPRN) to integrate comprehensive priors to regularize and optimize the solution space of SSR. Basically, the core framework is delicately assembled by several multiresidual relation blocks (MRBs) that fully facilitate the transmission and utilization of the low-frequency content prior of RGBs. Innovatively, the semantic prior of RGB inputs is introduced to mark category attributes, and a semantic-driven spatial relation module (SSRM) is invented to perform the feature aggregation of clustered similar ranges for refining recovered characteristics. In addition, we develop a transformer-based channel relation module (TCRM), which breaks the habit of employing scalars as the descriptors of channelwise relations in the previous deep feature prior and replaces them with certain vectors to make the mapping function more robust and smoother. In order to maintain the mathematical correlation and spectral consistency between hyperspectral bands, the second-order prior constraints (SOPCs) are incorporated into the loss function to guide the HSI reconstruction. Finally, extensive experimental results on four benchmarks demonstrate that our HPRN can reach the state-of-the-art performance for SSR quantitatively and qualitatively. Furthermore, the effectiveness and usefulness of the reconstructed spectra are verified by the classification results on the remote sensing dataset. Codes are available at https://github.com/Deep-imagelab/HPRN.

A neural network framework for portfolio optimization under second-order stochastic dominance

Traditional portfolio optimization strategies often rely on statistical methods and linear programming tools to achieve a balance between return and risk. Despite their usefulness for portfolio optimization, they cannot efficiently capture the specific differences and complexity of real-world financial markets. Several modern approaches attempt to overcome these limitations by using nonlinear models, machine learning, and advanced risk measures. In this study, we propose a novel strategy for optimizing portfolios that incorporates second-order stochastic dominance constraints and solves them with neural networks. we show that portfolios subject to second-order stochastic dominance constraints outperform their traditional counterparts, especially in tail-risk situations.

Adjustable light robust optimization with second order stochastic dominance constraints

Robust optimization suffers from excessive conservatism and infeasibility due to stringent requirements on all constraints within the uncertainty set, rendering robust solutions impractical. The light robust approach has been proposed to mitigate these challenges. This method aims to identify a solution that minimizes the weighted sum of all constraint violations while adhering to a predetermined limit on the deterioration of expected return. Drawing inspiration from light robustness, our paper introduces the adjustable light robust optimization models with second-order stochastic dominance constraints. We empirically examine their feasibility, out-of-sample performance, and the dynamic trade-off between return and robustness.

Investments in transmission lines and storage units considering second-order stochastic dominance constraints

Increasing intermittent renewable generation to meet the climate goals entails a deep transformation of current power systems. The transmission system must adapt to ensure a rapid and flexible response to the changes in the energy flows. Flexibility can be provided by reinforcing the interconnection among all the market agents and/or by installing facilities with fast response to the changes. In this work, we study the investment problem of a central planner that seeks to expand the transmission network and install storage units considering decarbonizing measures. We propose a two-stage stochastic problem with uncertainty on the demand growth and including representative days to characterize the hourly demand and renewable power variability. To obtain better expansion strategies according to a limit on the carbon emissions, second-order stochastic dominance constraints are imposed. Numerical analyses based on the power system of the Canary island (Spain) are provided. The results show that to install storage units is key to efficiently integrate renewable generation. The investments in the transmission system are mostly in lower-voltage lines. The formulation with stochastic dominance constraints results in higher second-stage investments, allowing a better adaptation to the demand growth evolution.

Improving texture integrity through second-order constraints on warping maps

Pose Transfer has recently gained significant attention, particularly for its user-friendly applications in the animation industry. The primary objective is to transform a given RGB image into a new target pose. This process involves two consecutive tasks: initially, warping the image to approximately align with the target pose, and subsequently using this rough estimation to generate a photorealistic image of the input in the desired pose.The primary challenge lies in the first task, where the image undergoes a rough transformation to its new location in the target pose. Current deep learning approaches rely on first-order warping, employing an affine transformation to move all image pixels. Despite yielding promising results, this approach has significant challenges when dealing with complex deformations, mainly due to the simplistic nature of its linear function. In contrast, we suggest transferring patches using a set of correlation layers. In each layer, the warping for each pixel of the image is individually estimated. We additionally introduce a constraint aimed at minimizing the energy of second derivatives across the entire warping map of the pixels. This allows for keeping the integration of local textures following the warping process, a feature already ensured in the affine-based transformation by restricting the transition to a linear function for all the image pixels. Our approach not only preserves the integrity of local textures, akin to the affine transformation, but achieves this by individually estimating the warping for each image pixel, thereby enabling finer adjustments of the input sample to the target pose. We illustrate the superior performance of this technique compared to affine-based strategies on the renowned DeepFashion database.

A Novel Trajectory Tracking Control of AGV Based on Udwadia-Kalaba Approach

Several control approaches have been used in order to achieve the trajectory tracking control of automated guided vehicle (AGV). But they are all based on the D'Alembert principle which requires to determine the Lagrangian multipliers. Unlike those control methods, in this paper, a novel approach of trajectory tracking control is presented, which is based on Udwadia-Kalaba approach. This approach presents a novel, concise and explicit equation of motion for constrained mechanical systems with holonomic and/or nonholonomic constraints as well as constraints that may be ideal or non-ideal. The Udwadia-Kalaba equation is uncoupled and free from the Lagrangian multipliers. In this paper, we classify constraints into structural constraints and performance constraints. Structural constraints are set up regardless of trajectory control and we use structural constraints to establish the dynamic model. Then the desired trajectory is set as performance constraints and constraint torques are solved by analyzing Udwadia-Kalaba equation. For AGV, a nonholonomic mechanical system, second-order constraints are used to get constraint forces and the numerical simulation is conducted by using Matlab. The results show that the AGV's movement meets the requirement and the tracking trajectory is exact and perfect. Compared with other approaches, this approach requires very little computation. Through two cases of tracking a circle and a line, how to use Udwadia-Kalaba equation to realize trajectory tracking control is shown in detail.

A second-order exponential integration constraint energy minimizing generalized multiscale method for parabolic problems

This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial discretization of the model problem using constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). This approach consists of two stages. First, the auxiliary space is constructed by solving local spectral problems, where the basis functions corresponding to small eigenvalues are captured. The multiscale basis functions are obtained in the second stage using the auxiliary space by solving local energy minimization problems over the oversampling domains. The basis functions have exponential decay outside the corresponding local oversampling regions. We shall consider the first and second-order explicit exponential Runge-Kutta approach for temporal discretization and to build a fully discrete numerical solution. The exponential integration strategy for the time variable allows us to take full advantage of the CEM-GMsFEM as it enables larger time steps due to its stability properties. We derive the error estimates in the energy norm under the regularity assumption. Finally, we will provide some numerical experiments to sustain the efficiency of the proposed method.

Impact of induced magnetic field on Darcy–Forchheimer nanofluid flows comprising carbon nanotubes with homogeneous-heterogeneous reactions

The appealing traits of carbon nanotubes (CNTs) encompassing mechanical and chemical steadiness, exceptional electrical and thermal conductivities, lightweight, and physiochemical reliability make them desired materials in engineering gadgets. Considering such stimulating characteristics of carbon nanotubes, our goal in the current study is to scrutinize the comparative analysis of Darcy–Forchheimer nanofluid flows containing CNTs of both types of multi and single-wall carbon nanotubes (MWCNTs, SWCNTs) immersed into two different base fluids over a stretched surface. The originality of the model being presented is the implementation of the induced magnetic field that triggers the electric conductivity of carbon nanotubes. Moreover, the envisioned model is also analyzed with homogeneous-heterogeneous (h-h) chemical reactions and heat source/sink. The second-order slip constraint is assumed at the boundary of the surface. The transmuted high-nonlinearity ordinary differential equations (ODEs) are attained from the governing set of equations via similarity transformations. The bvp4c scheme is engaged to get the numerical results. The influence of different parameters is depicted via graphs. For both CNTs, the rate of heat flux and the surface drag coefficient are calculated using tables. It is highlighted that an increase in liquid velocity is witnessed for a varied counts volume fraction of nanoparticles. Also, Single-wall water-based carbon nanotube fluid has comparatively stronger effects on concentration than the multi-walled carbon nanotubes in water-based liquid. The analysis also indicates that the rate of heat flux and the surface drag coefficient are augmented for both SWCNTs and MWCNTs for different physical parameters. The said model is also validated by comparing it with a published result.

Convex Formulation and Efficiency Enhancement for Powered Landing Guidance with Second-order Cone Probability Constraints

Convex Formulation and Efficiency Enhancement for Powered Landing Guidance with Second-order Cone Probability Constraints

Some Estimates for the Jump of the Derivative of the Lagrange Multiplier Function in Optimal Control Problems with Second-order State Constraints

Some Estimates for the Jump of the Derivative of the Lagrange Multiplier Function in Optimal Control Problems with Second-order State Constraints

Path-Constrained Time-Optimal Motion Planning for Robot Manipulators With Third-Order Constraints

Planning time-optimal motions of robot manipulators is important for maximizing productivity in industry and has attracted much attention in academia. Time-optimal time scaling (TOTS) of specified paths subject to second-order constraints is a well-studied problem in robotics. However, there is still a lack of effective approaches for computing TOTS with higher order constraints. This article proposes a novel method for TOTS subject to third-order constraints. The proposed method formulates the third-order TOTS as a four-stage optimization involving only linear programming by exploiting the special structure of the problem. The proposed method first performs a backward pass and a forward pass to generate the second-order optimal velocity profile. Then, the points violating the third-order constraints are identified, and the constraint violations are eliminated through numerical integration around the violating points. A bisection search algorithm is proposed to quickly determine the switching points at which the elimination process begins. The proposed method is verified through numerical examples and experimental tests. The results indicate that the proposed method outperforms the state-of-the-art approaches in terms of solution quality and computation time.

Improvement on the axial force accuracy of the ANCF Euler-Bernoulli beam element with the second-order approximate function of the centerline and precise constraint equations

The conventional Euler-Bernoulli beam element of the absolute nodal coordinate formulation (ANCF) yields incorrect axial force due to the existence of the first-order approximate function of the centerline and over-constraint equations. This work aims to improve the axial force accuracy of the element by using the second-order centerline approximate function and precise constraint equations. The second-order function includes the quintic Hermite shape function and the vector of nodal coordinates containing zeroth to second-order derivatives of position. The elastic force vector of the element and its tangent stiffness were then formulated based on the decoupled elastic line method. The exact kinematic requirements of three types of constraint points were fully clarified. On this basis, the corresponding concise constraint equations, constraint Jacobian and Hessian matrices were rigorously derived in the context of ANCF, where G2 continuity was demonstrated to be satisfied at the node acted by an inclined concentrated force, the relative rotation constraint of the rigid joint was described using the dot product of the gradients on both sides of the joint, and the fixing gradient direction at the partially-clamped end was expressed by using the zero cross product of the end gradients in the initial and deformed configurations. Large deformation problems of typical beams under fixed and follower loads were solved using five types of elements, where the results of the ABAQUS B22 elements were taken as a reference for validation. It is found that when using the first- and second-order beam elements having over-constraint equations of the three types of constraint points, obvious axial force error occurs near the corresponding constraint points. In comparison, a few second-order elements containing the derived constraint equations output correct axial force consistent with ABAQUS. However, a large number of the first-order elements containing the correct constraint equations still yield inaccurate axial force in certain beam regions.

Formation tracking of multi-robot systems with switching directed topologies based on Udwadia-Kalaba approach

In this paper, a distributed formation tracking protocol is proposed for multi-robot systems with switching directed topologies based on the Udwadia-Kalaba approach. The basic idea is to use the consensus-based scheme to reconstruct formation tracking control requirement into a second-order constraint first, and then apply the Udwadia-Kalaba approach to obtain the constraint force required to achieve the formation tracking, and afterward derive the explicit equations of motion for the constrained multi-robot systems for the control algorithm design. The convergence analysis of the tracking error system is conducted to affirm that the proposed control algorithm can achieve the formation tracking when the switching directed topologies have a directed spanning tree across each switching time interval. Numerical simulations are performed to validate the effectiveness of the proposed algorithm.

Distributionally robust joint chance-constrained programming: Wasserstein metric and second-order moment constraints

In this paper, we propose a new approximate linear reformulation for distributionally robust joint chance programming with Wasserstein ambiguity sets and an efficient solution approach based on Benders decomposition. To provide a convex approximation to the distributionally robust chance constraint, we use the worst-case conditional value-at-risk constrained program. In addition, we derive an approach for distributionally robust joint chance programming with a hybrid ambiguity set that combines a Wasserstein ball with second-order moment constraints. This approach, which allows injecting domain knowledge into a Wasserstein ambiguity set and thus allows for less conservative solutions, has not been considered before. We propose two formulations of this problem, namely a semidefinite programming and a computationally favorable second-order cone programming formulation. The models and algorithms proposed in this paper are evaluated through computational experiments demonstrating their computational efficiency. In particular, the Benders decomposition algorithm is shown to be more than an order of magnitude faster than a standard solver allowing for the solution of large instances in a relatively short time.

Efficient Allocation and Sizing the PV-STATCOMs in Electrical Distribution Grids Using Mixed-Integer Convex Approximation

Photovoltaic (PV) systems are a clean energy source that allows for power generation integration into electrical networks without destructive environmental effects. PV systems are usually integrated into electrical networks only to provide active power during the day, without taking full advantage of power electronics devices, which can compensate for the reactive power at any moment during their operation. These systems can also generate dynamic reactive power by means of voltage source converters, which are called PV-STATCOM devices. This paper presents a convex formulation for the optimal integration (placement and sizing) of PV-STATCOM devices in electrical distribution systems. The proposed model considers reducing the costs of the annual energy losses and installing PV-STATCOM devices. A convex formulation was obtained to transform the hyperbolic relation between the products of the voltage into a second-order constraint via relaxation. Two simulation cases in the two IEEE test systems (33- and 69-node) with radial and meshed topologies were implemented to demonstrate the effectiveness of the proposed mixed-integer convex model. The results show that PV-STATCOM devices reduce the annual cost of energy losses of electrical networks in a more significant proportion than PV systems alone.

New Constraint Qualifications for Mathematical Programs with Second-Order Cone Complementarity Constraints

New Constraint Qualifications for Mathematical Programs with Second-Order Cone Complementarity Constraints

Robust reward-risk performance measures with weakly second-order stochastic dominance constraints

Robust reward-risk performance measures with weakly second-order stochastic dominance constraints

Analytical modeling of vertical distribution of streamwise velocity in open channels using fractional entropy

Following the work of Chiu based on classical Shannon entropy, several kinds of generalized entropies have been explored in literature for studying open-channel flow. In this work, we explore a new kind of entropy, namely fractional entropy, which is based on the popular fractional calculus, to derive the vertical distribution of streamwise velocity in open channels. The velocity profile is derived analytically using the series approximation for the Lambert function. Also, the entropy index (i.e., the order of the fractional derivative) is considered a varying parameter and is computed along with the Lagrange multipliers by solving a nonlinear system using the second-order moment constraint, i.e., the momentum balance equation. The derived velocity equation is validated with selected laboratory and field data and compared with the Shannon, Tsallis, and Renyi entropy-based velocity profiles. It is observed that the proposed model can predict the measured values well for all the cases and the model corresponding to the entropy-based momentum coefficient formula is superior to all the abovementioned models. Further, the effects of Lagrange multipliers and the entropy index on the velocity profile are discussed. Also, the entropy index values for all the data are not close to zero, which specializes the entropy into the classical Shannon entropy, and hence, the approach justifies the applicability of the fractional entropy over the Shannon entropy in the context of open-channel flow velocity. Moreover, the methodology is developed based on an approximation of the series, which is based on a convergence criterion. This criterion needs to be verified against each of the data sets and, therefore, may become a difficult task for handling large data sets. To address this issue, this study provides a possible way of reformulating the mathematical model in terms of a nonlinear system with inequality constraint as a scope for future research. Finally, it is expected that the study can be further extended to study other kinds of important hydraulic variables such as sediment concentration, shear stress, etc.

Optimal real-time tuning of autonomous distributed power systems using modern techniques

This work considers using a novel heuristic population-based evolutionary algorithm [viz., the moth flame optimization (MFO) algorithm] to regulate the conventional controller installed in an autonomous power system (APS). The moth flame optimization algorithm intends to produce the optimal magnitudes of the proportional-integral-derivative plus second derivative (PIDD2) controller parameters along with its first- and second-order low-pass filter constraints (installed in the investigated autonomous power system). The present task includes a comparison of the voltage response profiles of the investigated system obtained by the proposed moth flame optimization-based proportional-integral-derivative plus second derivative controller and those obtained by other algorithms (conveyed in current state-of-the-art literature) based on a proportional-integral controller. A fast-acting Sugeno fuzzy logic (SFL) technique is used to achieve the dynamic online results of the investigated autonomous power system model for online, off-nominal operational circumstances. Under step perturbations, the time-domain transient investigation in reference to voltage and/or mandate of load for the proposed autonomous power system model is inspected. Additionally, the robustness of the proposed moth flame optimization-based proportional-integral-derivative plus second derivative controller is investigated to test its behavior. An investigation has been provided by varying the model components of the studied autonomous power system model. It may be reported, as per the results obtained from the simulation, that the proposed moth flame optimization-based proportional-integral-derivative plus second derivative controller is an effective control strategy for the autonomous power system. The current research effort indicates that the proposed moth flame optimization algorithm, along with Sugeno fuzzy logic, may be useful for the actual time process of an autonomous power system.