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Front. Inform. Technol. Electron. Eng.  2018, Vol. 19 Issue (11): 1444-1458    DOI:
    
Hohmann transfer via constrained optimization
Li XIE, Yi-qun ZHANG, Jun-yan XU
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources,
School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China
Beijing Institute of Electronic Systems Engineering, Beijing 100854, China
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Abstract  Inspired by the geometric method proposed by Jean-Pierre MAREC, we first consider the Hohmann
transfer problem between two coplanar circular orbits as a static nonlinear programming problem with an inequality
constraint.  By the Kuhn-Tucker theorem and a second-order sufficient condition for minima, we analytically prove
the global minimum of the Hohmann transfer.  Two sets of feasible solutions are found:  one corresponding to the
Hohmann transfer is the global minimum and the other is a local  minimum.   We next formulate the Hohmann
transfer problem as boundary value problems, which are solved by the calculus of variations. The two sets of feasible
solutions are also found by numerical examples.  Via static and dynamic constrained optimizations,  the solution
to the Hohmann transfer problem is re-discovered, and its global minimum is analytically verified using nonlinear
programming.

Key words： Hohmann transfer      Nonlinear programming      Constrained optimization      Calculus of variations     
Received: 11 May 2018      Published: 13 June 2019
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Li XIE
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Jun-yan XU
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Li XIE, Yi-qun ZHANG, Jun-yan XU. Hohmann transfer via constrained optimization. Front. Inform. Technol. Electron. Eng., 2018, 19(11): 1444-1458.

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Hohmann transfer via constrained optimization

Inspired by the geometric method proposed by Jean-Pierre MAREC, we first consider the Hohmann
transfer problem between two coplanar circular orbits as a static nonlinear programming problem with an inequality
constraint.  By the Kuhn-Tucker theorem and a second-order sufficient condition for minima, we analytically prove
the global minimum of the Hohmann transfer.  Two sets of feasible solutions are found:  one corresponding to the
Hohmann transfer is the global minimum and the other is a local  minimum.   We next formulate the Hohmann
transfer problem as boundary value problems, which are solved by the calculus of variations. The two sets of feasible
solutions are also found by numerical examples.  Via static and dynamic constrained optimizations,  the solution
to the Hohmann transfer problem is re-discovered, and its global minimum is analytically verified using nonlinear
programming.

关键词： Hohmann transfer,  Nonlinear programming,  Constrained optimization,  Calculus of variations 
[1] Cheng-gang Cui, Yan-jun Li, Tie-jun Wu. A relative feasibility degree based approach for constrained optimization problems[J]. Front. Inform. Technol. Electron. Eng., 2010, 11(4): 249-260.