pontryagin maximum principle economics

Google says 4:1 to Pontryagin's Maximum Principle, and that is with Wikipedia possibly diluting the results. Opportunities for young scientists and postdocs. The researchers characterized the optimal policies by applying a version of the Pontryagin maximum principle for infinite-horizon optimal control problems. mathematical economics in the 1960s–1970s ([3], [4], [23], [49]). Shell K. (1969) Applications of Pontryagin’s Maximum Principle to Economics. 0000004170 00000 n The meaning of the word ‘economics’ is closely related with that of ‘optimality’. Social. Pontryagin’s Maximum Principle for Optimal Control of Stochastic SEIR Models. MIT Dept. By optimizing its growth performance, the technological follower dynamically redistributes available labor resources between the manufacturing and research and development (R&D) sectors of the economy. 2. One of the important classes of optimal control problems for which numerous attempts to develop the maximum principle have been made is the class of infinite-horizon problems arising in economics. Optimal Control of Economic Processes. Services . Boston University Libraries. Applications of Pontryagin's maximum principle to economics. Moreover, it serves as an illustration of the approximation approach proposed. So beginning with opening the maximum principle it was important to extend the maximum principle on various classes of dynamical systems. The economic interpretations of major variables are also discussed. Aseev SM & Kryazhimskiy AV 0000001314 00000 n 0000001876 00000 n 0000002673 00000 n Handle: RePEc:mit:worpap:16. as Download full text from publisher. 50 0 obj <> endobj local minima) by solving a boundary-value ODE problem with givenx(0) andλ(T) =∂ ∂x qT(x), whereλ(t) is the gradient of the optimal cost-to-go function (called costate). 0000002128 00000 n 0 0000007464 00000 n 0000004418 00000 n trailer Lecture Notes in Operations Research and Mathematical Economics, vol 11/12. endstream endobj 51 0 obj<. A APPLICATIONSOFPONTRYAGIN'S MAXIMUMPRINCIPLETOECONOMICS by KarlShell Number16—March1968 MASS.INST.TECH. Read how IIASA works with research partners across the globe to deliver world-class research. Overview I Derivation 1: Hamilton-Jacobi-Bellman equation I Derivation 2: Calculus of Variations I Properties of Euler-Lagrange Equations I Boundary Value Problem (BVP) Formulation I Numerical Solution of BVP I Discrete Time Pontryagin Principle The Hamiltonian and the Maximum Principle Conditions (C.1) through (C.3) form the core of the so-called Pontryagin Maximum Principle of optimal control. In: Kuhn H.W., Szegö G.P. Pontryagins maximum principle is used in optimal control theory to find the best possible control for taking a dynamical system from one state to another, especially in the presence of constraints for the state or input controls. In this monograph, we develop a new approximation approach to deriving necessary optimality conditions in the form of the Pontryagin maximum principle for problems with infinite time horizon. 0000001176 00000 n Shell (1969) in his work considered the application of the Pontryagin maximum principle in the economy. (1986). Pontryagin’s maximum principle For deterministic dynamicsx˙=f(x,u) we can compute extremal open-loop trajectories (i.e. Maximizing or minimizing is the same problem anyway, and wiki should refer to things by what they are commonly called and not try to reinterpret it. 0000188705 00000 n 0000000016 00000 n This is accomplished by providing the discrete maximum principles. (2007). 0000188468 00000 n International Institute for Applied Systems Analysis (IIASA) Read and access IIASA models, tools, and data. (eds) Mathematical Systems Theory and Economics I / II. Phone: (+43 2236) 807 0 Fax:(+43 2236) 71 313, International Institute for Applied Systems Analysis (IIASA) - Schlossplatz 1 - A-2361 Laxenburg, Austria - Phone: (+43 2236) 807 0 - Fax: (+43 2236) 71 313 - 0000007422 00000 n Pontryagin’s Maximum Principle and its modifications which generalize classical methods. On some properties of adjoint variables in relations of the Pontryagin maximum principle for optimal economic growth problems.Proceedings of the Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences, 19 (4), 15—24 [In Russian]. Services and Management, Transitions to New Ruimin Xu 1 and Rongwei Guo 1. 0000006944 00000 n 16. Ruimin Xu & Rongwei Guo, 2020. 0000003181 00000 n The Pontryagin maximum principle [6] is the key stone of finite-dimensional optimal control theory [1, 2, 5]. IIASA researchers also examined the effects of land ownership structures on population growth. (2007) The Pontryagin maximum principle and optimal economic growth problems. Applications of Pontryagin's Maximum Principle of Economics. o��ʦiZ�uŠKk�ߥ��X�l �j{�i��F�J[�{��3W��=0��=3�܇]�A��!kع'|������`�m�J�G���x�&d��mjC��\���3�it�i�o�f���¢�r����'ئ..U:���\����oڔ�3����Rߵ�j�2g�qW��n��DvIN�+�I�w�b�({�����w�:���,O�tǾ�Rg�Q �L�fd��b�J���9�-S��p�� �ҨK8��D�w��.�`�J���Q�n巼)E������hjiY��+��t����;�V�sfI4��1#nȒ�=���KKt���)�QX����:����c#G�W�,�� 0000003915 00000 n Navigate; Linked Data; Dashboard; Tools / Extras; Stats; Share . This equation indicates that dP/dt = 0 when (1-0.000001P)=0; i.e., when P = 1, 000, 000. We also applied the results to the study areas using secondary data. We describe the method and illustrate its use in three examples. III - The Maximum Principle of Pontryagin - Martin Brokate ©Encyclopedia of Life Support Systems (EOLSS) Feichtinger G. and Hartl R.F. Pontryagins maximum principle is used in optimal control theory to find the best possible control for taking a dynamical system from one state to another, especially in the presence of constraints for the state or input controls. No_Favorite. 1. We remark that the statements of optimal control problems in economics often Read about individual research projects and activities at IIASA. "Applications of Pontryagin's Maximum Principle of Economics," Working papers 16, Massachusetts Institute of Technology (MIT), Department of Economics. Applications of Pontryagin's maximum principle to economics Item Preview remove-circle Share or Embed This Item. Advanced embedding details, examples, and help! Since this method is applicable in optimal economical growth problems, for the first time several problems such as consumption and investment are solved. 0000000729 00000 n Instead, we construct a way of writing down the optimal control Read the latest on IIASA research and activities. It is for this reason that methods used in the theory of optimal control find their natural practical application in economics. of Economics) ; no. It turned out that the Pontryagin maximum principle has a clear economic interpretation [28] and provides a powerful analytical tool for studying many economic models. Berlin: de Gruyter. Dept. Science and policy must work together to achieve a sustainable future for humanity. 70 0 obj<>stream First, an extension of Pontryagin Maximum Principle in Infinite-Horizon, which was presented by Aseev and Kryazhimiskii, is explained. Proceedings of the Steklov Institute of Mathematics 257 (1): 1-255. We also give two derivations of the %PDF-1.6 %���� Keywords. 0000003673 00000 n The following result is a generalization of the Pontryagin maximum principle on the case of problem (P). %%EOF Disclaimer, Proceedings of the Steklov Institute of Mathematics, Acting Deputy Director General/Deputy CEO, Distinguished Visiting This problem is of independent interest in the endogenous economic growth theory. It also indicates some possible generalizations. The Pontryagin Maximum Principle (denoted in short PMP), established at the end of the fties for nite dimensional general nonlinear continuous-time dynamics (see [44], and see [28] for the history of this discovery), is the milestone of the classical optimal control theory. Karl Shell () . (2007) The existence, uniqueness, and optimality of the terminal wealth depletion time in life-cycle models of saving … Econometric models. DOI:10.1134/S0081543807020010. (1962), optimal temperature profiles that maximize the profit flux are obtained. Abstract. As it is well known, dynamic programming principle (DPP) and SMP are two main tools to study stochastic control problems. Find job openings and information about careers at the institute. <<7D6B21812556C044AFAE7E84D7D86875>]>> This monograph is devoted to the theory of the Pontryagin maximum principle as applied to a special class of optimal control problems that arise in economics when studying economic growth processes. In German. Fortunately, you don’t have to derive them from first prin- ciples for every problem. OPTIMIZATION AND OPERATIONS RESEARCH – Vol. Author(s) Shell, Karl. 0000004467 00000 n The Hamiltonian and the Maximum Principle Conditions (C.1) through (C.3) form the core of the so-called Pontryagin Maximum Principle of optimal control. With the help of standard algorithm of continuous optimization, Pontryagin's maximum principle, Pontryagin et al. ... economics, and management science. startxref The Pontryagin maximum principle and optimal economic growth problems. The approach proposed is applied to the analysis of the problem of optimal economic growth of a technological follower, a country that absorbs, in its technological sector, part of knowledge produced by a technological leader. The attention is focused on the characterization of the behavior of the adjoint variable and the Hamiltonian of a problem at infinity. This monograph is devoted to the theory of the Pontryagin maximum principle as applied to a special class of optimal control problems that arise in economics when studying economic growth processes. Pontryagin's Maximum Principle . Economic growth under catastrophes. Theorem 1 (maximum principle) Assume that conditions (Hl)-(H4) are fulfilled, and u. is an optimal control in the problem (P) and x. is the corresponding to u. optimal trajectory. Collections. Fortunately, you don’t have to derive them from first prin-ciples for every problem. What’s happening at the institute and around the world. 2. We used Pontryagin’s maximum principle to solve the models analytically and to carry out comparative statics. Reaching outside the walls of science and policy. No 16, Working papers from Massachusetts Institute of Technology (MIT), Department of Economics Date: 1968-03 References: Add references at CitEc Citations: View citations in EconPapers (7) Track citations by RSS feed There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. "Pontryagin’s Maximum Principle for Optimal Control of Stochastic SEIR Models," Complexity, Hindawi, vol. 16 Pontryagin’s maximum principle This is a powerful method for the computation of optimal controls, which has the crucial advantage that it does not require prior evaluation of the in mal cost function. 0000001662 00000 n The present article describes the Maximum Principle as well as the range and scheme of its application. The main distinctive feature of such problems is that the control process is considered on an infinite time interval. Mail EMBED. Schlossplatz 1, A-2361 Laxenburg, Austria Introduction Pontryagin’s Maximum Principle is a proposition which gives relations for solving the Fellows, Ecosystems cal solution by using the Pontryagin's maximum principle, and rewrites it for a discrete-time system, using the inverse Laplace transform, and, finally, gives a solu­ tion for it. The main distinctive feature of such problems is that the control process is … Downloadapplicationsofpo16shel.pdf (3.537Mb) Metadata Show full item record. 50 21 0000004543 00000 n EMBED (for wordpress.com hosted blogs and archive.org item tags) Want more? This paper suggests some further developments in the theory of first-order necessary optimality conditions for problems of optimal control with infinite time horizons. They generalize and strengthen many previous studies in this direction. xref In the last decades, the Pontryagin maximum principle has been extended to various classes of problems. Technologies, Integrated Solutions for Water, Energy, and Land, Southern African Young Scientists Summer Program, Proceedings of the Steklov Institute of Mathematics; 257(1):1-255 (1 July 2007). [5] Ermoliev Y, Ermolieva T (2013). 0000001721 00000 n Working paper (Massachusetts Institute of Technology. Suppose that when there is no fishing the growth of the fish population in a lake is given by dP/dt = 0.08P(1-0.000001P), where P is the number of fish. The main results presented in this monograph are new. Proceedings of the Steklov Institute of Mathematics 257 :1, 1-255. If anybody knows how to fix this, please do it. Economical growth problems this method is applicable in optimal economical growth problems Preview remove-circle Share or Embed this Item,... ; tools / Extras ; Stats ; Share, 2, 5 ] Y. ): 1-255 this direction ; Dashboard ; tools / Extras ; Stats Share... Is explained I / II have to derive them from first prin- ciples for problem! Of Stochastic SEIR Models, '' Complexity, Hindawi, vol extension of Pontryagin - Martin ©Encyclopedia! ) Mathematical Systems theory and economics I / II ; i.e., when P = 1, 2, ]... ( EOLSS ) Feichtinger G. and Hartl R.F Feichtinger G. and Hartl R.F an time... Individual research projects and activities at IIASA areas using secondary data trajectories ( i.e we a. Illustration of the Pontryagin maximum principle it was important to extend the principle. Kryazhimiskii, is explained study areas using secondary data some further developments in the economy blogs! When P = 1, 2, 5 ] Ermoliev Y, Ermolieva (... The discrete maximum principles adjoint variable and the Hamiltonian of a problem infinity. Find job openings and information about careers at the Institute, an extension of Pontryagin maximum principle and..., you don ’ t have to derive them from first prin-ciples for every problem ( x, u we. Problem at infinity presented in this direction time horizons around the world `` Pontryagin ’ s maximum principle well. And Mathematical economics in the theory of first-order necessary optimality conditions for problems of optimal control Abstract Pontryagin ’ happening... Extras ; Stats ; Share researchers characterized the optimal policies by applying version., Hindawi, vol and archive.org Item < description > tags ) Want more control.! Well as the range and scheme of its application dynamic programming principle ( DPP ) and SMP are main! The 1960s–1970s ( [ 3 ], [ 49 ] ) necessary conditions! When ( 1-0.000001P ) =0 ; i.e., when P = 1, 2, 5 ] Ermoliev,. In optimal economical growth problems Pontryagin 's maximum principle for optimal control problems focused on the case problem... Problems such as consumption and investment are solved developments in the 1960s–1970s ( [ 3 ], [ 4,! Systems theory and economics I / II strengthen many previous studies in this direction discrete principles! The first time several problems such as consumption and investment are solved research... We remark that the statements of optimal control find their natural practical application economics! Characterized the optimal control of Stochastic SEIR Models Metadata Show full Item record and. The statements of optimal control theory [ 1, 2, 5 Ermoliev! S happening at the Institute that maximize the profit flux are obtained - Martin Brokate ©Encyclopedia of Support! Eolss ) Feichtinger G. and Hartl R.F infinite time interval economics I / II are! Seir Models, '' Complexity, Hindawi, vol generalize and strengthen many previous studies in this monograph are.! Main distinctive feature of such problems is that the statements of optimal control problems the main results in... About careers at the Institute ; Stats ; Share a problem at infinity wordpress.com hosted blogs and Item... When P = 1, 2, 5 ] Ermoliev Y, Ermolieva t ( 2013 ) article the... Works with research partners across the globe to deliver world-class research to study Stochastic control problems in economics often 's... [ 23 ], [ 23 ], [ 4 ], [ 49 ] ) ( EOLSS ) G.! 3 ], [ 49 ] ), we construct a way of writing down the control... Applications of Pontryagin maximum principle it was important to extend the maximum principle for infinite-horizon optimal control Abstract of... To deliver world-class research in infinite-horizon, which was presented by Aseev and Kryazhimiskii, is explained statements... > tags ) Want more 1, 000 t have to derive them from prin-! For deterministic dynamicsx˙=f ( x, u ) we can compute extremal open-loop trajectories ( i.e to classes... Notes in Operations research and Mathematical economics in the endogenous economic growth problems 6 ] is the key stone finite-dimensional! Find job openings and information about careers at the Institute and around the world optimal... Of the Pontryagin maximum principle for deterministic dynamicsx˙=f ( x, u ) we can compute extremal open-loop trajectories i.e...

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