Multiplier Vector Research Articles

Prediction of Traffic Flow in Vehicular Ad-hoc Networks using Optimized Based-Neural Network

Traffic flow prediction is crucial for managing traffic, reducing pollution, ensuring public safety, and is a vital element of Intelligent Transportation Systems. Furthermore, the variables that influence traffic patterns (such as public events, road closures, and accidents) are predominantly unforeseen, rendering the prediction of traffic flow an intricate undertaking. The objective of this research is to enhance the accuracy of traffic flow forecast by employing a novel strategy that utilizes feedforward Neural-Networks and the Quasi-Newton method for optimization. The proposed strategy decreases the error factor based on the Lagrange multiplier and Jacobian vector. This enhancement has resulted in expedited convergence throughout the process of learning. The sample was chosen using datasets provided by the Traffic Monitoring System, specifically from Highway England, Performance Measurement System, and Maryland 511, for the year 2023. In order to assess the proposed model, the research outcomes are juxtaposed with other established prediction methodologies. The study revealed that the research model that was established performed better than previous prediction strategies based on measures of mean absolute error and root mean squared error.

On linear codes with random multiplier vectors and the maximum trace dimension property

Abstract Let C C be a linear code of length n n and dimension k k over the finite field F q m {{\mathbb{F}}}_{{q}^{m}} . The trace code Tr ( C ) {\rm{Tr}}\left(C) is a linear code of the same length n n over the subfield F q {{\mathbb{F}}}_{q} . The obvious upper bound for the dimension of the trace code over F q {{\mathbb{F}}}_{q} is m k mk . If equality holds, then we say that C C has maximum trace dimension. The problem of finding the true dimension of trace codes and their duals is relevant for the size of the public key of various code-based cryptographic protocols. Let C a {C}_{{\boldsymbol{a}}} denote the code obtained from C C and a multiplier vector a ∈ ( F q m ) n {\boldsymbol{a}}\in {\left({{\mathbb{F}}}_{{q}^{m}})}^{n} . In this study, we give a lower bound for the probability that a random multiplier vector produces a code C a {C}_{{\boldsymbol{a}}} of maximum trace dimension. We give an interpretation of the bound for the class of algebraic geometry codes in terms of the degree of the defining divisor. The bound explains the experimental fact that random alternant codes have minimal dimension. Our bound holds whenever n ≥ m ( k + h ) n\ge m\left(k+h) , where h ≥ 0 h\ge 0 is the Singleton defect of C C . For the extremal case n = m ( h + k ) n=m\left(h+k) , numerical experiments reveal a closed connection between the probability of having maximum trace dimension and the probability that a random matrix has full rank.

On value efficiency analysis and targeted benevolence cross efficiency

In this article, we examine the relation between cross efficiency and Value Efficiency Analysis, two Data Envelopment Analysis related models for peer appraisal assessment. Particularly, we show that the Targeted Benevolence cross efficiency formulation is equivalent to the Value Efficiency Analysis model if either (i) the “reference” unit, i.e. the one whose vector of optimal multipliers is used to evaluate all others in the Targeted Benevolence formulation, or (ii), its radial projection if it is inefficient, is chosen as the Most Preferred Solution in Value Efficiency Analysis. An immediate implication of this result is an alternative and most frequently shorter way to compute the Targeted Benevolence cross-efficiency matrix, as we can do so by solving a series of Value Efficiency Analysis problems, each of which uses a different unit or its radial projection if it is not efficient as the Most Preferred Solution. For this purpose, we provide a four-step algorithm, from which it is clear that in most of the cases it is not necessary to solve all the relevant problems. This depends on the number of inefficient units that are (radially) projected in the strongly efficient frontier and the number of different sets of peers for these units.

Optimal sliding mode controller for lower limb rehabilitation exoskeleton in constrained environments

<p>In this article, a lower limb exoskeleton (LLE) under contacting constrained motion has been modelled using augmented Lagrange equations which include Lagrange multiplier and Jacobian vectors. A sliding mode Controller optimized by the grey Wolf optimization algorithm has been used for controlling (LLE) in the case of constrained motion with uncertainties and outside perturbation. The grey wolf optimization algorithm has been used as an optimization algorithm for finding the optimal controllers’ parameters in order to improve the performance of the system. The stability analysis of the closed-loop system has been performed using Lyapunov theory of stability. To validate the effectiveness of the proposed controller structure grey wolf optimization algorithm controller (GW-SMC), a series of comparative simulations have been carried out with other types of recently existing sliding mode control (SMC). The results of numerical simulations indicate the superiority of the sliding mode optimized by the GW-SMC over other types of recently existing controller in terms of tracking errors and robustness towards uncertainties and external disturbances.</p>

Analysis of Wide-Frequency Dense Signals Based on Fast Minimization Algorithm

To improve the detection speed for wide-frequency dense signals (WFDSs), a fast minimization algorithm (FMA) was proposed in this study. Firstly, this study modeled the WFDSs and performed a Taylor-series expansion of the sampled model. Secondly, we simplified the sampling model based on the augmented Lagrange multiplier (ALM) method and then calculated the augmented Lagrange function of the sampling model. Finally, according to the alternating minimization strategy, the Lagrange multiplier vector and the sparse block phasor in the function were iterated individually to realize the measurement of the original signal components. The results show that the algorithm improved the analysis accuracy of the WFDS by 35% to 46% on the IEEE C37.118.1a-2014 standard for the wide-frequency noise test, harmonic modulation test, and step-change test, providing a theoretical basis for the development of the P-class phasor measurement unit (PMU).

Energy-Efficient Resource Allocation for Application Including Dependent Tasks in Mobile Edge Computing

This paper studies a single-user Mobile Edge Computing (MEC) system where mobile device (MD) includes an application consisting of multiple computation components or tasks with dependencies. MD can offload part of each computation-intensive latency-sensitive task to the AP integrated with MEC server. In order to accomplish the application faultlessly, we calculate out the optimal task offloading strategy in a time-division manner for a predetermined execution order under the constraints of limited computation and communication resources. The problem is formulated as an optimization problem that can minimize the energy consumption of mobile device while satisfying the constraints of computation tasks and mobile device resources. The optimization problem is equivalently transformed into solving a nonlinear equation with a linear inequality constraint by leveraging the Lagrange Multiplier method. And the proposed dual Bi-Section Search algorithm Bi-JOTD can efficiently solve the nonlinear equation. In the outer Bi-Section Search, the proposed algorithm searches for the optimal Lagrangian multiplier variable between the lower and upper boundaries. The inner Bi-Section Search achieves the Lagrangian multiplier vector corresponding to a given variable receiving from the outer layer. Numerical results demonstrate that the proposed algorithm has significant performance improvement than other baselines. The novel scheme not only reduces the difficulty of problem solving, but also obtains less energy consumption and better performance.

Schwarz Inequality Method for Weighted Minimum Effort Terminal Control of Multidimensional Systems

This study presents major developments in relation to problem dimensionality and formulation generality, endowing the Schwarz-inequality-based approach for finite-horizon minimum effort control with an extended degree of applicability. The extension of the Schwarz inequality method is mainly based on considering the static Lagrange multiplier that combines multiple terminal constraint relations as a vector. The minimum effort cost including a positive definite weighting function is then shown to be closely related to an associated Rayleigh quotient of the Lagrange multiplier vector. Investigation on the Rayleigh quotient form results in a simple expression for the optimal Lagrange multiplier vector, and thereby gives the closed-loop optimal control law in a time-varying state feedback form with a feedforward term. The proposed vector-based formalism provides as a direct consequence a unified means of design that encompasses several existing results developed for low-dimensional problems based on scalar-based formalism and also enables potential new developments in optimal trajectory shaping guidance.

An efficient model for locating solid waste collection sites in urban residential areas

A new model for the efficient collection of solid waste in urban residential areas is proposed as a set covering facility location problem. The model finds the optimal location of waste collection sites such that all the customers are covered. An important feature of the model is that, rather than aggregate the quantity of waste from a group of demand points, it is assumed that the volume of waste of different types is known for each customer. This assumption encourages point-of-collection sorting which helps provide an improved solution to the problem of waste collection. A Lagrangian relaxation (LR) of the problem was developed, and the resulting dual problem was solved using an LR procedure in which the vectors of Lagrangian multipliers were updated through the subgradient optimisation. A simple linear relaxation heuristic was developed to obtain a feasible solution to the primal problem. Five newly constructed datasets mimicking the scenario of a local municipality were used to test the efficiency of the model and the solution technique. Preliminary results and comparison with existing results showed that the proposed model is efficient as considerable reductions were obtained for the total number of activated collection sites and allocated containers.

Stock Market Price and the Performance of the Residential Property Market in Kenya

The purpose of the study was to assess the effect of stock market price on the performance of the residential property market in Kenya. The surge of the residential property prices in Kenya has ignited concerns about the affordability of residential property houses in Kenya. The escalation of residential property prices raises question as to whether it is in tandem with other markets in the Country especially the stock market. Researchers have inconclusive findings on the direction of causation or the strength of the relationship between stock market and performance of residential property market in Kenya. This study adopted a positivist philosophical attitude using causal research design. The study used quarterly secondary data from 2005 to 2018. The study employed vector error correction residual serial correlation langrange multiplier test and vector error residual heteroskedasticity test as the diagnostic tests. Vector error correction model and auto-regressive distributed lag model were employed to test the hypothesis in the short run and long run respectively. The study found that stock market price had a negative effect on performance of residential property market in Kenya in the short term suggesting substitution effect while in the long run stock market price had a positive effect on the performance of residential property market in line with the wealth effect. The study concludes that stock market information spills over and affects residential property market performance in Kenya both in the long run and short run. The study has also contributed to the confounding empirical and theoretical literature and narrowed the research gap especially on the conflicting substitution effect and wealth effect of stock market and residential property market performance in Kenya. Keywords: Stock Market Price, Performance, Residential Property Market DOI : 10.7176/RJFA/10-18-15 Publication date :September 30 th 2019

Inverse Anti-$k$-centrum Problem on Networks with Variable Edge Lengths

This paper concerns the problem of modifying edge lengths of a network at minimum total costs so as to make a prespecified vertex become an optimal location in the modified environment. Here, we focus on the ordered median objective function with respect to the vector of multipliers $\lambda = (1,\ldots,1,0,\ldots,0)$ with $k$ 1's. This problem is called the inverse anti-$k$-centrum problem. We first show that the inverse anti-$k$-centrum problem is NP-hard even on tree networks. However, for the inverse anti-$k$-centrum problem on cycles, we formulate it as one or two linear programs, depending on odd or even integer $k$. Concerning the special cases with $k = 2,3,M$, we develop combinatorial algorithms that efficiently solve the problem, where $M$ is the number of vertices of the cycle.

Scaled constraint qualifications for generalized equation constrained problems and application to nonsmooth mathematical programs with equilibrium constraints

In this paper, the notion of graphical derivatives is applied to define a new class of several well-known constraint qualifications for a nonconvex multifunction M at a point of its graph. This class is called as “scaled constraint qualifications”. The reason of this terminology is that these conditions ensure the existence of bounded KKT multiplier vectors with a proper upper bound. The relations between these constraint qualifications and stability properties of M are also investigated. New sharp necessary optimality conditions with bounded multiplier vectors are derived for an optimization problem with a generalized equation constraint. The results are adapted to nonsmooth general constrained problems and nonsmooth mathematical programs with equilibrium constraints.

A dynamic condensation method with free interface substructuring

Abstract In this paper, a novel dynamic condensation method is proposed with free interface substructuring, in which the substructures are completely decoupled. The substructures are independently defined and the substructural finite element (FE) models are individually reduced by adopting the improved reduced system (IRS) method. The reduced mass and stiffness matrices of substructures are assembled using a Lagrange multiplier vector, leading to the final reduced model. Using the proposed method, each of the substructural FE models can be reduced in parallel without coupling among the neighboring substructures. Thus, the method can be applied with ease to substructures connected through non-matching meshes. Moreover, complicated substructural interfaces can be accommodated when employing this method. The formulation of the proposed method is presented in detail, and its accuracy, computational efficiency, and modeling ability are investigated using several demonstrative engineering problems.

A distributed asynchronous method of multipliers for constrained nonconvex optimization

This paper presents a fully asynchronous and distributed approach for tackling optimization problems in which both the objective function and the constraints may be nonconvex. In the considered network setting each node is active upon triggering of a local timer and has access only to a portion of the objective function and to a subset of the constraints. In the proposed technique, based on the method of multipliers, each node performs, when it wakes up, either a descent step on a local augmented Lagrangian or an ascent step on the local multiplier vector. Nodes realize when to switch from the descent step to the ascent one through an asynchronous distributed logic-AND, which detects when all the nodes have reached a predefined tolerance in the minimization of the augmented Lagrangian. It is shown that the resulting distributed algorithm is equivalent to a block coordinate descent for the minimization of the global augmented Lagrangian. This allows one to extend the properties of the centralized method of multipliers to the considered distributed framework. Two application examples are presented to validate the proposed approach: a distributed source localization problem and the parameter estimation of a neural network.

Proper or Weak Efficiency via Saddle Point Conditions in Cone-Constrained Nonconvex Vector Optimization Problems

Motivated by many applications (for instance, some production models in finance require infinity-dimensional commodity spaces, and the preference is defined in terms of an ordering cone having possibly empty interior), this paper deals with a unified model, which involves preference relations that are not necessarily transitive or reflexive. Our study is carried out by means of saddle point conditions for the generalized Lagrangian associated with a cone-constrained nonconvex vector optimization problem. We establish a necessary and sufficient condition for the existence of a saddle point in case the multiplier vector related to the objective function belongs to the quasi-interior of the polar of the ordering set. Moreover, exploiting suitable Slater-type constraints qualifications involving the notion of quasi-relative interior, we obtain several results concerning the existence of a saddle point, which serve to get efficiency, weak efficiency and proper efficiency. Such results generalize, to the nonconvex vector case, existing conditions in the literature. As a by-product, we propose a notion of properly efficient solution for a vector optimization problem with explicit constraints. Applications to optimality conditions for vector optimization problems are provided with particular attention to bicriteria problems, where optimality conditions for efficiency, proper efficiency and weak efficiency are stated, both in a geometric form and by means of the level sets of the objective functions.

A roller bearing fault diagnosis method using interval support vector deterministic optimization based on nested PSO

An interval support vector deterministic optimization model (ISVD) is proposed for the fault classification problem of uncertainty samples in this paper. Firstly, based on the order relation theory, support vector machines using interval samples is transformed into ISVD, which is a two-objective optimization problem, with the midpoint and the radius optimized at the same time. Then, ISVD is converted into a single objective optimization model by the linear combination. The single objective optimization model includes Lagrange multiplier vector and interval sample vectors, both of which are nested. Thus, the nested particle swarm optimization (PSO) based on dynamic decreasing inertia weight is applied to select the optimal Lagrange multiplier vector of this model. Lastly, the effectiveness of the proposed method is proved by the data set of University of California Irvine (UCI) and the roller bearing fault experiments. The experimental results show: ISVD owns outstanding generalization ability with the help of the structured risk minimization and global optimization. The accuracy of the proposed ISVD is better than that of the native Bayes uncertain classification method 1 (NBU1), native Bayes uncertain classification method 2 (NBU2) and the formula-based Bayes classifier (FBC).

Two‐echelon distribution systems with random demands and storage constraints

We consider a general two‐echelon distribution system consisting of a depot and multiple sales outlets, henceforth referred to as retailers, which face random demands for a given item. The replenishment process consists of two stages: the depot procures the item from an outside supplier, while the retailers' inventories are replenished by shipments from the depot. Both of the replenishment stages are associated with a given facility‐specific leadtime. The depot as well as the retailers faces a limited inventory capacity. Inventories are reviewed and orders are placed on a periodic basis. When a retailer runs out of stock, unmet demand is backlogged.We propose a new approach to the above class of dynamic programming models based on Lagrangian relaxation. Every choice of the vector of Lagrange multipliers generates a lower bound via the solution of a single dynamic program (DP) with a one‐dimensional state‐space. The best such bound is obtained by maximizing over the vector of multipliers. The strategy that is optimal for this (maximal) lower bound DP employs an (s, S) ordering policy (generally, with time‐dependent policy parameters). To arrive at an upper bound and an implementable heuristic, this (s, S) policy is paired with one of several possible allocation policies that allocate the system‐wide inventory across the different facilities.We report on an extensive numerical study with close to 14 000 instances which evaluates the accuracy of the lower bound and the optimality gap of the various heuristic policies. The study reveals that the lower bound and the heuristic strategy that is constructed on its basis perform exceedingly well, almost across the entire parameter spectrum, including instances where demands are rather volatile or the average cycle time between consecutive orders is relatively large. The exception arises when storage at the depot is as expensive as at the retailer level and the retailers have large storage capacities.

Evidence of Large-Scale Social Interactions in Mammography in the United States

This paper examines the extent of social interactions in an individual’s decision to undergo mammography. Using Behavioral Risk Factors Surveillance System surveys from 1993 to 2016, the effect of other female screening behavior on an individual’s decision to have a routine breast cancer screening was measured by calculating the size of a so called “social multiplier” in mammography. A vector of social multipliers was estimated in the use of mammograms in the past 1–2 years by taking the ratio of group-level effects of exogenous explanatory variables to individual-level effects of the same variables. Peer groups were defined as same-aged women living in the same state. Three age groups of women were considered: 40–49, 50–74, and 75 and older. Several econometric approaches were used to analyze the effect of social interactions on mammography use, including ordinary least squares, fixed effects, and split-sample instrumental variable. For all women, evidence was found of social interactions associated with individual’s education, employment, and poor health. In addition, number of age-group-specific social multipliers was found. The strongest evidence of spillover in mammography was found for women ages 75 and older. Policy makers should be aware that, in the presence of a social multiplier, the value of any type of screening intervention is higher than the one that would be measured at the individual-level.

Directional Distance Functions in DEA with Optimal Endogenous Directions

This paper is concerned with optimal directions in the directional distance function in data envelopment analysis. It is shown that the vector pointing in the direction that minimizes the Euclidean distance between the input–output vector (Xo, Yo) and the efficient frontier, the input isoquant reflecting output Yo, or the output isoquant reflecting input Xois optimal, because the corresponding vector of virtual multipliers defines the relative prices that maximize profit, cost, or revenue efficiency. The associated efficiency indicator is a value measure of technical efficiency in difference form with the Euclidean distance between (Xo, Yo) and the efficient frontier, the Yoinput isoquant, or the Xooutput isoquant as an equivalent directional distance quantity indicator. A linear combinatorial optimization program for computing the relevant value indicators of technical efficiency in multiplier space or the equivalent quantity indicators in terms of the relevant Euclidean distances is developed. A nonlinear and nonconvex optimization model for an estimation of the relevant value indicator of efficiency in multiplier space is also developed. Preliminary computational results are reported.

On Global Dynamics of Three Dimensional Magnetohydrodynamics: Nonlinear Stability of Alfvén Waves

Magnetohydrodynamics (MHD) studies the dynamics of magnetic fields in electrically conducting fluids. In addition to the sound wave and electromagnetic wave behaviors, magneto-fluids also exhibit an interesting phenomenon: They can produce the Alfven waves, which were first described in a physics paper by Hannes Alfven in 1942. Subsequently, Alfven was awarded the Nobel prize for his fundamental work on MHD with fruitful applications in plasma physics, in particular the discovery of Alfven waves. This work studies (and constructs) global solutions for the three dimensional incompressible MHD systems (with or without viscosity) in strong magnetic backgrounds. We present a complete and self-contained mathematical proof of the global nonlinear stability of Alfven waves. Specifically, our results are as follows: We obtain asymptotics for global solutions of the ideal system (i.e.,viscosity \(\mu =0\)) along characteristics; in particular, we have a scattering theory for the system. We construct the global solutions (for small viscosity \(\mu \)) and we show that as \(\mu \rightarrow 0\), the viscous solutions converge in the classical sense to the zero-viscosity solution. Furthermore, we have estimates on the rate of the convergence in terms of \(\mu \). We explain a linear-driving decay mechanism for viscous Alfven waves with arbitrarily small diffusion. More precisely, for a given solution, we exhibit a time \(T_{n_0}\) (depending on the profile of the datum rather than its energy norm) so that at time \(T_{n_0}\) the \(H^2\)-norm of the solution is small compared to \(\mu \) (therefore the standard perturbation approach can be applied to obtain the convergence to the steady state afterwards). The results and proofs have the following main features and innovations: We do not assume any symmetry condition on initial data. The size of initial data (and the a priori estimates) does not depend on viscosity \(\mu \). The entire proof is built upon the basic energy identity. The Alfven waves do not decay in time: the stable mechanism is the separation (geometrically in space) of left- and right-traveling Alfven waves. The analysis of the nonlinear terms are analogous to the null conditions for non-linear wave equations. We use the (hyperbolic) energy method. In particular, in addition to the use of usual energies, the proof relies heavily on the energy flux through characteristic hypersurfaces. The viscous terms are the most difficult terms since they are not compatible with the hyperbolic approach. We obtain a new class of space-time weighted energy estimates for (weighted) viscous terms. The design of weights is one of the main innovations and it unifies the hyperbolic energy method and the parabolic estimates. The approach is ‘quasi-linear’ in nature rather than a linear perturbation approach: the choices of the coordinate systems, characteristic hypersurfaces, weights and multiplier vector fields depend on the solution itself. Our approach is inspired by Christodoulou–Klainerman’s proof of the nonlinear stability of Minkowski space-time in general relativity.

Three dimensional elements with Lagrange multipliers for the modified couple stress theory

Three dimensional mixed elements for the modified couple stress theory are proposed. The $$C^{1}$$ continuity for the displacement field, which is required because of the curvature term in the variational form of the theory, is satisfied weakly by introducing a supplementary rotation as an independent variable and constraining the relation between the rotation and the displacement with a Lagrange multiplier vector. An additional constraint about the deviatoric curvature is also considered for three dimensional problems. Weak forms with one constraint and two constraints are derived, and four elements satisfying convergence criteria are developed by applying different approximations to each field of independent variables. The elements pass a patch test for three dimensional problems. Numerical examples show that the additional constraint could be considered essential for the three dimensional elements, and one of the elements is recommended for practical applications via the comparison of the performances of the elements. In addition, all the proposed elements can represent the size effect well.