Szennyezési jogok hatása a vállalati termelési stratégiára = Effect of pollution rights on production strategy of firm

A cikk a szennyezési jogok bevezetését vizsgálja a mikroökonómia standard vállalatára. A komparatív statika módszerével vizsgáljuk a termelő vállalat lehetséges reakcióit a szennyezési jog bevezetésére. A vállalatok stratégiája a szennyezési jog bevezetésére a technológia változatlanul hagyása, vagy megváltoztatása lehet. Az egyes esetekben arra keresünk választ, hogy hogyan változik a vállalat nyeresége a bevezetés előtti állapothoz képest, és ez milyen szennyezési stratégiával jár. Szennyezési jogot elad-e, vagy vesz a vállalat a szennyezési jogok piacán? = The paper deals with the effect of an introduction of tradable permits on the production strategy of a firm. It is assumed that the firm will maximize its profit. After introducing the emission trading the profit function will contain the linear emission procurement/selling costs. We will compare the optimal production strategy before tradable permits and after that. The mathematical investigation is based on the nonlinear mathematical programming.

Digital design of heat-resistant dimensionally stable carbon laminate (CFRP) structures

Special features of designing heat-resistant dimensionally stable structures are considered. A new design procedure is proposed, in which finite elements are used as a language for describing the load-bearing structure of a construction and the distribution of material in it considering the possibility of setting the desired structure of a composite material. The design task is formulated in terms of nonlinear mathematical programming. A sequence of digital models is used for its approximate solution in the interactive mode. The specific features of finite element modeling of thin-walled structures made of laminated composite material are discussed. The technique is demonstrated using the example of the development of a large-size space telescope body.

Determination of the Optimal Values of the Parameters of Linear Corrective Devices of the Automatic Control System by the Integral Quadratic Criterion

When designing an automatic control system (ACS), it is important to determine the optimal values of the parameters of the correcting device according to any of the criteria. Recently, more and more publications have appeared on the use of the method of nonlinear mathematical programming for solving problems of synthesis of an automated control system. The article discusses a method for determining the optimal parameters of linear correcting devices according to the quadratic integral criterion. The novelty is the presentation of the above mentioned problem in the form of a nonlinear mathematical programming problem. To find a multiparametric, multiextremal, i.e. complex, objective function, a random search method is used. Also, a class of automatic control systems having one extreme objective function is highlighted. For this case, the theorems are proved, and the formula for determining extreme points is given in an analytical form. Numerical examples are also considered. Programs have been developed for implementing the corresponding algorithms on a computer in VBA language. The graphs of the corresponding transients are given.

STIFFNESS ANALYSIS AND OPTIMIZATION OF STEPPED COLUMNS UNDER COMBINED BENDING AND COMPRESSION

The paper presents the stiffness analysis and optimization of stepped columns constituting the core frame of the industrial building. The two-span cross section of a one- storey industrial building is investigated herein. The quasi-static calculation is performed using the limited load approximation method for the cross-section of the most loaded middle column. The critical Euler characteristic of the compressive longitudinal load is determined by the differential bending equations at the bifurcation instability in the column sections. The parameter optimization of the column cross-section is achieved through the nonlinear mathematical programming. The optimization of medium column cross-section is considered using the proposed calculation when setting a set of constraints for the optimization task.

A Simplified C-Logit Stochastic User Equilibrium Model on Bimodal Transportation Network

This paper investigates the C-logit stochastic user equilibrium (SUE) problem on a bimodal transportation network with road and rail travel modes. The C-logit model captures the overlapping effect among the different paths via commonality factors; sequentially, it has ability to obtain a more realistic traffic flow distribution pattern. In this paper, when we redefine the link travel cost functions and employ a binary Logit model for the mode split, the bimodal C-logit SUE model can be simplified into an unconstrained nonlinear mathematical programming formulation. Such model is verified to satisfy the bimodal C-logit SUE conditions at its stationary point and can be solved by existing algorithms. So, the simplified model can be convenient to be used on the general bimodal transportation network.

A Multistage Feedback Control Strategy for Producing 1,3-Propanediol in Microbial Continuous Fermentation

In this paper, we consider a multistage feedback control strategy for producing 1,3-propanediol in microbial continuous fermentation. Both the dilution rate and the concentration of glycerol in the input feed are used as control variables, and these variables are further assumed to be in the form of a linear combination of biomass and glycerol concentrations. Unlike the general form of linear feedback control, the coefficients of linear combination are continuous functions with respect to time. Inspired by the control parameterization method, we use the piecewise-constant functions to approximate the coefficient functions; then we get the multistage feedback control law by solving nonlinear mathematical programming problems. Numerical results indicate the flexibility and effectiveness of our strategy.

Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem

In this paper, we modified a Courant-Beltrami penalty function method for constrained optimization problem to study a duality for convex nonlinear mathematical programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions for the penalized problem has been used to derived KKT multiplier based on the imposed additional hypotheses on the constraint function g. A zero-duality gap between an optimization problem constituted by invex functions with respect to the same function η and their Lagrangian dual problems has also been established. The examples have been provided to illustrate and proved the result for the broader class of convex functions, termed invex functions.

Stress-strain state analysis and optimization of rod system under periodic pulse load

The paper considers the problem of analysis and optimization of rod systems subjected to combined static and periodic pulse load. As a result of the study the analysis method was developed based on traditional approach to solving homogeneous matrix equations of state and a special algorithm for developing a particular solution. The influence of pulse parameters variations on stress-strain state of a rod system was analyzed. Algorithms for rod systems optimization were developed basing on strength recalculation and statement and solution of optimization problem as a problem of nonlinear mathematical programming. Recommendations are developed for efficient organization of process for optimization of rod systems under static and periodic pulse load.

Photovoltaic Cell Parameters Identification Using Nonlinear Mathematical Programming

This paper proposes a mathematical programming based approach for optimal estimation of photovoltaic cell model parameters. In this study, solar cell models are used to represent the current-voltage characteristics of the solar cell. The model is represented as a non-linear function that relates the cell current and voltage with some parameters to be estimated. No direct general analytical solution exists for such function. Given the input-output characteristic data of the solar cell, a mathematical programming technique is used to solve a set of transcendental equations to optimally estimate the solar cell parameters.