Pontryagin’s Type Optimality Conditions for a Distributed Control Problem Arising in Endogenous Growth Theory

Author(s):  
Bernhard Skritek ◽  
Tsvetomir Tsachev ◽  
Vladimir M. Veliov
2008 ◽  
Vol 01 (02) ◽  
pp. 131-146 ◽  
Author(s):  
G. M. Bahaa

A distributed control problem for cooperative parabolic systems governed by Schrödinger operator is considered. The performance index is more general than the quadratic one and has an integral form. Constraints on controls are imposed. Making use of the Dubovitskii-Milyutin Theorem given by Walczak (1984, On some control problems Acta Univ. Lod. Folia Math., 1, 187-196), the optimality conditions are derived for the Neumann problem. Finally, several mathematical examples for derived optimality conditions are presented.


Author(s):  
Nguyen Thi Thuc An ◽  
Dau Kieu Ngoc Anh

The 2018 Nobel Economics Prize was awarded to two American economists - William D. Nordhaus and Paul M. Romer - who designed methods for better assessing environmental issues and technological advances on growth. This year’s Laureates, Nordhaus was the first person to create an intergrated model to assess interactions between society and nature and Romer laid the foundation for what is now called endogenous growth theory. According to the Swedish Royal Academy of Sciences, these two macroeconomists’ research have helped “significantly broaden the scope of economic analysis by constructing models that explain how the market economy interacts with nature and knowledge” which integrates climate change measures into long-term sustainable economic growth. Keywords Nobel in economics, William D. Nordhaus, Paul M. Romer, climate change, endogenous growth theory, economic growth References [1] Y Vân (2018), “Lý lịch 'khủng' của hai nhà khoa học vừa giành giải Nobel Kinh tế 2018”, Vietnambiz, đăng tải ngày 08/10/2018, https://vietnambiz.vn/ly-lich-khung-cua-hai-nha-khoa-hoc-vua-gianh-giai-nobel-kinh-te-2018-95776.html[2] Jonas O. Bergman, Rich Miller (2018), “Nordhaus, Romer Win Nobel for Thinking on Climate, Innovation”, đăng tải ngày 8/10/2018, https://www.bloomberg.com/news/articles/2018-10-08/nordhaus-romer-win-2018-nobel-prize-in-economic-sciences [3] Antonin Pottier (2018), “Giải Nobel” William Nordhaus có thật sự nghiêm túc?”, Nguyễn Đôn Phước dịch, đăng tải ngày 11/10/2018, http://www.phantichkinhte123.com/2018/10/giai-nobel-william-nordhaus-co-that-su.html[4] Thăng Điệp (2018), “Giải Nobel kinh tế 2018 về tay hai người Mỹ”, đăng tải ngày 8/10/2018, http://vneconomy.vn/giai-nobel-kinh-te-2018-ve-tay-hai-nguoi-my-20181008185809239.htm[5] Lars P. Syll (2018), “Cuối cùng - Paul Romer cũng có được giải thưởng Nobel”, Huỳnh Thiện Quốc Việt dịch, đăng tải ngày 14/10/2018, http://www.phantichkinhte123.com/2018/10/cuoi-cung-paul-romer-cung-co-uoc-giai.html[6] Phương Võ (2018), “Nobel Kinh tế 2018: Chạm tới bài toán khó của thời đại”, đăng tải ngày 9/10/2018, https://nld.com.vn/thoi-su-quoc-te/nobel-kinh-te-2018-cham-toi-bai-toan-kho-cua-thoi-dai-20181008221734228.htm[7] Đông Phong (2018), “Nobel Kinh tế cho giải pháp phát triển bền vững và phúc lợi người dân”, đăng tải ngày 8/10/2018, https://news.zing.vn/nobel-kinh-te-cho-giai-phap-phat-trien-ben-vung-va-phuc-loi-nguoi-dan-post882860.html[8] Thanh Trúc (2018), “Giải Nobel kinh tế 2018: Thay đổi tư duy về biến đổi khí hậu”, https://tusach.thuvienkhoahoc.com/wiki/Gi%E1%BA%A3i_Nobel_kinh_t%E1%BA%BF_2018:_Thay_%C4%91%E1%BB%95i_t%C6%B0_duy_v%E1%BB%81_bi%E1%BA%BFn_%C4%91%E1%BB%95i_kh%C3%AD_h%E1%BA%ADu[9] Cẩm Anh (2018), “Nobel kinh tế 2018: Lời giải cho tăng trưởng kinh tế bền vững”, đăng tải ngày 11/10/2018, http://enternews.vn/nobel-kinh-te-2018-loi-giai-cho-tang-truong-kinh-te-ben-vung-137600.html.


10.1038/1982 ◽  
1998 ◽  
Vol 4 (9) ◽  
pp. 995-999
Author(s):  
Terence Kealey ◽  
Aram Rudenski

Sign in / Sign up

Export Citation Format

Share Document