Chapter2, mainly summarizing the optimality conditions for the nonconvex semidefinite programming, first recalls the concept of transversality condition, proves that transversality condition and linear independence condition are equivalent, and shows that under strict complementarity condition, the transversality condition is a sufficient condition for uniqueness of the Lagrange multipliers.

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Based on Pontryagin maximum principle, the lunar soft landing problem is transformed into a two-point boundary value problem in mathematics. In consideration of the bound condition and transversality condition, the resulted two-point boundary value problem is converted into a parameter optimization problem aiming at the initial values of conjugate variables and the terminal time, then it is solved by the nonlinear programming.

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Chapter3, being the main part of this dissertation, converts nonconvex semidefinite programming problem to nonlinear programming problem, and proves that under transversality condition, strict complementarity condition and the sufficient optimality condition of local solutions, and are equivalent locally.

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condition of transversality：橫截性條件

橫截性|transversality | 橫截性條件|condition of transversality | 橫坐標(biāo)|abscissa