Dual Forecasting Algorithm for Technological Structural Matrices in Dynamic Input-Output Models

The purpose of the research. Amidst structural transformations in the global economy, increasing sanctions pressure, and the need to ensure technological sovereignty, the need for effective long-term strategic planning tools is growing. One such traditionally powerful tool is the input-output model. However, V.V. Leontief's classical static model fails to adequately account for the interrelationships between investment, accumulation, and the growth of the economy's production potential over time. The purpose of this study is to conduct a comprehensive theoretical and methodological analysis of key approaches, identify the problems and contradictions arising during the transition from a static to a dynamic input-output model, and assess the prospects for its application in solving pressing economic development challenges. The study draws on methods of systems and comparative analysis, a historical-economic approach, and economic-mathematical modeling. A critical review of classical and contemporary works in the field of the theory and practice of constructing an input-output model is provided. Conclusions. The study systematized the main methodological approaches to constructing a dynamic input-output model, such as the capacity dynamics model and models based on difference or differential equations. Key issues hindering the widespread practical application of the dynamic input-output model were identified and analyzed in detail. These include: the problem of model closure and the endogenous determination of investment demand; difficulties in estimating and volatility of the capital intensity matrix; accounting for investment lags and the time structure of capacity commissioning; and the integration of technological progress factors into the model. The need to develop adaptive hybrid dynamic input-output models integrated with big data analysis and scenario forecasting tools is substantiated to improve their adequacy in conditions of turbulence and uncertainty. The scientific novelty lies in the comprehensive structuring of the methodological problems of the dynamic model of inter-industry balance from the standpoint of both the theory and practice of their statistical support, as well as in the formulation of priority areas for modernization of the methodology in relation to the tasks of modern state strategic planning in Russia.

This paper describes a combined continuous-discrete simula tion model of an economy. The simulation model "solves" a dynamic input-output model (a system of differential equations) by numerically tracing the level of state variables through time. An analytic solution to this system, while possible, is imprac tical because of discontinuities in the state equations due to in dustry capacity constraints and irreversibilities in investment levels. The model is fitted with data for the Grant County Oregon economy and used to measure the dynamic impacts of an in crease in allowable timber harvest in the county. This study dem onstrates the advantages of the dynamic model over its static counterpart and explores its potential application to various economic impact problems.

Necessary and sufficient conditions are derived, which are fulfilled by quadratic functions that can be written as a product of two affine-linear functions plus an additive constant. This criterium characterizes convex and nonconvex quadratic programming problems, which can be solved by one ofSwarup's [1966a, 1966b, 1966c] algorithm.

This paper describes a new technique for generating convex, strictly concave and indefinite (bilinear or not) quadratic programming problems. These problems have a number of properties that make them useful for test purposes. For example, strictly concave quadratic problems with their global maximum in the interior of the feasible domain and with an exponential number of local minima with distinct function values and indefinite and jointly constrained bilinear problems with nonextreme global minima, can be generated. Unlike most existing methods our construction technique does not require the solution of any subproblems or systems of equations. In addition, the authors know of no other technique for generating jointly constrained bilinear programming problems.

Inference on estimators defined by mathematical programming

In this paper, we present a recurrent neural network for solving mixed linear complementarity problems (MLCPs) with positive semi-definite matrices. The proposed neural network is derived based on an NCP function and has a low complexity respect to the other existing models. In theoretical and numerical aspects, global convergence of the proposed neural network is proved. As an application, we show that the proposed neural network can be used to solve linear and convex quadratic programming problems. The validity and transient behavior of the proposed neural network are demonstrated by using five numerical examples.

The optimal control problem of linear quadratic regulation (the LQR problem) for linear discrete-time systems with single input delay is studied in this paper. A new and simple approach is applied to derive the optimal control input sequences. With the established duality, we first show that the LQR problem is equivalent to an optimization problem in Krein space. The latter problem is finally converted to a strictly convex quadratic programming problem. Thus we convert the delayed control input into control input delay-free, and convert a dynamic LQR optimal control problem for the linear discrete-time systems into a static mathematical programming model. The optimal control input sequences are successfully derived by solving this strictly convex quadratic programming problem. Our approach is simple and yet very effective in dealing with the LQR problem for the linear discrete-time systems with single input delay.

Forecasting of Russian Economy Development with Use of the Dynamic Input-Output Model with Fuzzy Parameters

Although the classical LQR design method has been very successful in real world engineering designs, in some cases, the classical design method needs modifications because of the saturation in actuators. This modified problem is sometimes called the constrained LQR design. For discrete systems, the constrained LQR design problem is equivalent to a convex quadratic programming problem with box constraints. We will show that the interior-point method is very efficient for this problem because an initial interior point is available, a condition which is not true for general convex quadratic programming problem. We will devise an effective and efficient algorithm for the constrained LQR design problem using the special structure of the box constraints and a recently introduced arc-search technique for the interior-point algorithm. We will prove that the algorithm is polynomial and has the best-known complexity bound for the convex quadratic programming. The proposed algorithm is implemented in MATLAB. An example for the constrained LQR design is provided to show the effectiveness and efficiency of the design method. The proposed algorithm can easily be used for model predictive control.

An optical reconfigurable intelligent surface (ORIS) was expected to offer extra secrecy performance gain in a visible light communication (VLC) system. However, nonlinear impairments involved degrade the confidential signal reception and have not been fully considered in designing physical layer security (PLS). In this paper, a novel PLS approach is proposed for an ORIS-aided VLC system with consideration of practical nonlinear impairments. It is mathematically formulated to be an optimization problem that maximizes the signal-to-interference-plus-distortion-and-noise ratio of the legitimate link, while entirely suppressing that of multiple eavesdroppers by jointly optimizing the beamforming, jamming and clipping at the transmitters, and also the surface configuration in terms of mirror assignments and rotation angles at the ORIS. We decompose this mixed combinatorial and non-convex optimization problem into three sub-problems and elaborately transform them to be conventional convex programming, quadratic programming and nonlinear programming problems, respectively. Moreover, we also develop a time-efficient iterative approach to achieve the suboptimal solution with low-computational complexity. Simulation results demonstrate the improvement of secrecy performance as compared with conventional schemes, and also the robustness to severe nonlinear impairments and spatial correlation, thereby confirming the beneficial insights of this methodology for secure VLC with nonlinear devices.

Iterative method for finding the balanced growth solution of the non-linear dynamic input–output model and the dynamic CGE model

ABSTRACT1 We consider a dynamic input output model that represents important aspects of Richard Cantillon’s discussion of economic structure and market dynamics. Merchants and inventories determine prices that diverge from (longer run) equilibrium. We contrast this stable formulation of price determination with an unstable benchmark specification in which variations in mercantile inventories play no role. Appreciated the stabilising properties of classical dynamics but did not isolate the influence of inventory behaviour. We briefly consider the role of inventories in macroeconomics, and note that balance sheet effects have rendered credit dislocations considerably more persistent than they were in Cantillon’s day.

The brain-computer interface (BCI) P300 speller analyzes the P300 signals from the brain to achieve direct communication between humans and machines, which can assist patients with severe disabilities to control external machines or robots to complete expected tasks. Therefore, the classification method of P300 signals plays an important role in the development of BCI systems and technologies. In this article, a novel ensemble support vector recurrent neural network (E-SVRNN) framework is proposed and developed to acquire more accurate and efficient electroencephalogram (EEG) signal classification results. First, we construct a support vector machine (SVM) to formulate EEG signals recognizing model. Second, the SVM formulation is transformed into a standard convex quadratic programming (QP) problem. Third, the convex QP problem is solved by combining a varying parameter recurrent neural network (VPRNN) with a penalty function. Experimental results on BCI competition II and BCI competition III datasets demonstrate that the proposed E-SVRNN framework can achieve accuracy rates as high as 100% and 99%, respectively. In addition, the results of comparison experiments verify that the proposed E-SVRNN possesses the best recognition accuracy and information transfer rate (ITR) compared with most of the state-of-the-art algorithms.

Although conceptually superior to its static counterpart, the dynamic input-output model has failed to achieve popularity due to its virtual inoperability. Key extensions to the Leontief dynamic model facilitate specification using numerical and simulation techniques. The extended model's operability and capabilities are demonstrated using county level data.

The strictly convex quadratic programming problem is transformed to the least distance problem — finding the solution of minimum norm to the system of linear inequalities. This problem is equivalent to the linear least squares problem on the positive orthant. It is solved using orthogonal transformations, which are memorized as products. Like in the revised simplex method, an auxiliary matrix is used for computations. Compared to the modified-simplex type methods, the presented dual algorithm QPLS requires less storage and solves ill-conditioned problems more precisely. The algorithm is illustrated by some difficult problems.