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Mathematical Modeling of Investments in an Imperfect Capital Market

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS 2021年第SUPPL 1期313卷 S175-S184页

作者： Shananin, A. A. Natl Res Univ Moscow Inst Phys & Technol Dolgoprudnyi 141701 Russia

We consider the problem of modeling the investments in an imperfect capital market in which the interest on loans significantly exceeds the interest on deposits. To determine the cash flow deflator, we propose to use the Cantor-Lippman model in which the investment environment is described by a pool of stationary and replicable projects. The pool of investment projects defines the investment function, which is built as the pointwise maximum of Laplace transforms of the cash flows of investment projects. The Cantor-Lippman model of investment in an imperfect capital market allows us to build a Bellman function, which can be used to assess the financial state of the investor. We study the properties of the Bellman operator in the problem of an optimal investment strategy. It is shown that the minimum positive root of the investment function should be used as a cash flow deflator. We also study a dynamic control system describing the investment process. Modes of balanced growth are built. The Neumann growth rate and the Neumann equilibrium states are determined. A weak turnpike theorem is proved.

关键词： investments Cantor-Lippman model mathematical modeling of economics NPV IRR Bellman operator investment polynomial linear programming problem

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Exponential stabilisation of positive singular linear discrete-time delay systems with bounded control

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IET CONTROL THEORY AND APPLICATIONS 2019年第7期13卷 905-911页

作者： Vu Ngoc Phat Nguyen Huu Sau VAST Inst Math 18 Hoang Quoc Viet Rd Hanoi Vietnam Hanoi Univ Ind Fac Sci 298 Caudien Hanoi Vietnam

Inspired by the results obtained in Liu et al. (2008, 2009), this study extends the constrained control problem to singular linear positive discrete-time systems with delay. By using the singular value decomposition approach, delay-dependent sufficient conditions for the regularity, causality, positivity and exponential stabilisation with a given decay rate of the system are established in terms of linear programming problem. A numerical example to demonstrate the effectiveness of the proposed method is given.

关键词： singular value decomposition asymptotic stability discrete time systems linear programming linear systems delay systems exponential stabilisation positive singular linear discrete-time delay systems bounded control constrained control problem singular linear positive discrete-time systems delay-dependent sufficient conditions linear programming problem singular value decomposition

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Tri-level transmission expansion planning under intentional attacks: virtual attacker approach - part I: formulation

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IET GENERATION TRANSMISSION & DISTRIBUTION 2019年第3期13卷 390-398页

作者： Nemati, Hadi Latify, Mohammad Amin Yousefi, Gholam Reza Isfahan Univ Technol Dept Elect & Comp Engn Esfahan *** Iran

The first part of this two-part paper proposes tri-level transmission expansion planning (TTEP) under physical intentional attacks. In the first level, the network planner looks for an optimal transmission expansion plan to fortify the power network. In the second level, the attacker tries to maximise damages to the network. In the third level, the adverse effects of the attacks on the network operation are minimised by the network operator. Since the third level problem is a linear programming (LP) problem, the second and third levels are converted into a single-level model by using primal-dual transformation, and consequently, TTEP is converted into a bi-level programming problem. To achieve a single-level model, instead of assuming a unique attacker, a cooperative game of multiple virtual attackers (VAs) of which every VA is to maximise the damage by attacking one transmission line is introduced and modelled. The conditions that enforce Nash and Pareto equilibria of this game are derived as linear constraints which are lower level equivalent. By using this equivalence, the aforementioned bi-level TTEP model is converted into a single-level model that can be recast as a mixed integer LP problem. The numerical results are provided in the second part.

关键词： integer programming linear programming power transmission planning game theory physical attacks network operator network operation linear programming problem single-level model bi-level programming problem multiple virtual attackers virtual attacker approach tri-level transmission expansion planning model physical intentional attacks network planner problem optimal transmission expansion plan power network bi-level TTEP model Pareto equilibrium Nash equilibrium linear constraints

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L1-gain control on positive impulsive system via a hybrid proportional plus integral algorithm

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IET CONTROL THEORY AND APPLICATIONS 2019年第7期13卷 898-904页

作者： Chen, Hao Zhan, Tao Huang, Qinzhen Southwest Minzu Univ Coll Elect & Informat Engn Chengdu 610041 Sichuan Peoples R China Univ Waterloo Dept Appl Math Waterloo ON N2L 3G1 Canada Shandong Univ Sch Math Jinan 250100 Shandong Peoples R China

In this study, the L1-gain control issues on positive system are investigated. A hybrid proportional impulsive with integral (PII) control scheme is proposed. This impulse-time-dependent control algorithm uses the proportional control action $K_p$Kp at impulse instants for stabilising, and applies the integral control strategy $K_{_I}$KI between impulse time intervals for improving the state convergence, respectively. The average impulsive interval approach and co-positive Lyapunov function method are employed to derive the sufficient conditions. Then L1-gain performance of the impulsive positive system can be guaranteed by solving the linear programming problem. In addition, iterative convex optimisation algorithm is presented for the design of PII control gain matrices. Numerical examples illustrate the expected results of this design.

关键词： Lyapunov methods matrix algebra gain control control system synthesis linear programming time-varying systems iterative methods convex programming stability impulse time intervals co-positive Lyapunov function method impulsive positive system iterative convex optimisation algorithm PII control gain matrices positive impulsive system hybrid proportional plus integral algorithm integral control scheme impulse-time-dependent control algorithm impulse instants impulsive interval approach integral control strategy o?'broken vertical bar(1) stability proportional control action K-p a"'(1)-gain control issues linear programming problem

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The Optimal Distribution problem for Teams of Specialists

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AUTOMATION AND REMOTE CONTROL 2019年第1期80卷 93-101页

作者： Burkov, V. N. Rossikhina, L. V. Vyunov, A. P. Rogovaya, L. V. Russian Acad Sci Trapeznikov Inst Control Sci Moscow Russia Voronezh Inst Fed Penitentiary Serv Voronezh Russia Fed Penitentiary Serv Cent Regulatory & Tech Lab Moscow Russia JSC Voronezhsintezkauchuk Res Ctr Voronezh Russia

We consider the task of assigning teams of specialists who jointly perform certain types of jobs (consulting services, compliance assessment for products, goods or services according to given requirements etc.). The team performing this work is composed of a set of specialists of various types (specialties), and their total number is limited. The problem is to design a team work plan for which the time to complete all jobs is minimal. We reduce this task to a linear programming problem and also consider heuristic algorithms and special cases of the problem.

关键词： team of specialists schedule set of teams linear programming problem

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Real time scheduler for multiprocessor systems based on continuous control using Timed Continuous Petri Nets ⁎

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IFAC-PapersOnLine 2020年第4期53卷 371-377页

作者： L. Rubio-Anguiano A. Ramírez-Treviño A. Chils J.L. Briz CINVESTAV-IPN Unidad Guadalajara Av. del Bosque 1145 CP 45019 Zapopan Jalisco Mexico DIIS/I3A Univ. de Zaragoza María de Luna 1 - 50018 Zaragoza España

This work exploits Timed Continuous Petri Nets (TCPN) to design and test a novel energy-efficient thermal-aware real-time global scheduler for a hard real-time (HRT) task set running on a multiprocessor system. The TCPN model encompasses both the system and task set, including thermal features. In previous work we calculated the share of each task that must be executed per time interval by solving off-line an Integer programming problem problem (ILP). A subsequent on-line stage allocated jobs to processors. We now perform the allocation off-line too, including an allocation controller and an execution controller in the on-line stage. This adds robustness by ensuring that actual task allocation and execution honor the safe schedule provided off-line. Last, the on-line controllers allow the design of an improved soft RT aperiodic task manager. Also, we experimentally prove that our scheduler yields fewer context switches and migrations on the HRT task set than RUN, a reference algorithm.

关键词： Real Time Scheduling Petri Net linear programming problem Unimodularity

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A linear programming APPROACH TOWARDS INDIVIDUATION LIGHTING SYSTEM WITH OPTIMAL ENERGY CONSUMPTION

A LINEAR PROGRAMMING APPROACH TOWARDS INDIVIDUATION LIGHTING...

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International Conference on Advanced Materials, Energy and Environmental Sustainability (ICAMEES)

作者： Divya, Chevikala Pai, Namratha Manipal Inst Technol Manipal Acad Higher Educ Dept Elect & Elect Engn Manipal 576104 Karnataka India

Energy consumption is considered to be scope for wide range of research. This paper is an attempt to the process of energy conservation in the field of lighting science. A classroom with multiple locations and different combinations of four luminaires were considered for the study. linear programming problem is used to optimize the energy consumption with respect to illuminance at particular location. This study depicts the relation between energy consumption and number of luminaires at certain location considering individual satisfaction as a dynamic factor. Result shows the effectiveness of the methodology on light energy consumption satisfying individual preferred illuminance. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： linear programming problem Energy conservation Individual preferred illuminance

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Improving the consistency of incomplete hesitant multiplicative preference relation

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OPSEARCH 2019年第1期56卷 324-343页

作者： Sahu, Mamata Gupta, Anjana Delhi Technol Univ Dept Appl Math Delhi 110042 India

As it know, most decision processes are depends on preference relations as in the forms by comparing different alternatives over criteria. In the process of decision making, a decision maker may give his/her judgement by means of hesitant multiplicative preference relation (HMPR) using the scale of 1/9-9 for hesitancy and uncertainty. Shortage of of time, experience and lack of the experts' professional knowledge lead to form an incomplete hesitant multiplicative preference relation. In this paper we have defined a multiplicative transitive property of HMPR that preserves the hesitancy property. Another aim of this paper is to characterise two different approaches to calculate the missing element of incomplete HMPR from the incomplete one. The first approach involves two step, estimating step calculate the initial values of the missing element and the adjusting step minimizing the error. A linear programming model is developed in the second approach to calculate the missing values of incomplete hesitant multiplicative preference relation. The satisfaction degree and the acceptable consistency of complete HMPR is also checked. The whole procedure is explained with a suitable example.

关键词： Multiplicative preference relation Hesitant multiplicative preference relation Hesitant multiplicative element linear programming problem Satisfaction degree Acceptable consistency

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A note on "A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem"

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APPLIED MATHEMATICAL MODELLING 2015年第19期39卷 5982-5985页

作者： Bhardwaj, Bindu Kumar, Amit Thapar Univ LM Thapar Sch Management Patiala 147004 Punjab India Thapar Univ Sch Math & Comp Applicat Patiala 147004 Punjab India

Ezzati et al. (2013) proposed a method for comparing triangular fuzzy numbers and using it, propose a new algorithm to find the fuzzy optimal solution of fully fuzzy linear programming problems with equality constraints. Ezzati et al. also claimed that the fuzzy optimal solution of fully fuzzy linear programming problems with inequality constraints can also be obtained by the same algorithm by transforming it into fully fuzzy linear programming problems with equality constraints. In this note, it is proved that the fully fuzzy linear programming problems with inequality constraints cannot be transformed into fully fuzzy linear programming problems with equality constraints and hence, the algorithm, proposed by Ezzati et al. to find the fuzzy optimal solution of fully fuzzy linear programming problems with equality constraints, cannot be used for finding the fuzzy optimal solution of fully fuzzy linear programming problems with inequality constraints. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Fully fuzzy linear programming problem

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Difference Schemes in the Undetermined Coefficient Space and Dual problems of linear programming

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2018年第6期58卷 827-839页

作者： Lobanov, A. I. Moscow Inst Phys & Technol Dolgoprudnyi 141700 Moscow Oblast Russia

Using properties of the difference schemes approximating a one-dimensional transport equation as an example, it is shown that optimization of the properties of difference schemes based on the analysis in the space of undetermined coefficients and optimization of these properties based on the method of parametric correction are dual problems. Hybrid difference schemes for the linear transport equation are built as solutions to dual linear programming problems. It is shown that Godunov's theorem follows from the linear program optimality criterion as one of the complementary slackness conditions. A family of hybrid difference schemes is considered. It is shown that Fedorenko's hybrid difference scheme is obtained by solving the dual linear programming problem.

关键词： linear transport equation difference scheme Fedorenko's hybrid scheme linear programming problem complementary slackness conditions monotonic schemes Lagrange multipliers Godunov's theorem

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