Continuation Method with the Trust-region Time-stepping Scheme for Linearly Constrained Optimization with Noise Data
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The nonlinear optimization problem with linear equality constraints has many applications in engineering fields such as the visual-inertial navigationand localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to solve this practical problem effectively, this paper constructs a semi-implicit continuation method with the trust-region time-stepping scheme for the linear equality constrained optimization subproblem at every iteration. Numerical results illustrate that the new method works well for this positioning problem with or without the measurement error, and the traditional sequential quadratic programming (SQP) method (the built-in subroutine fmincon.m of the MATLAB environment) fails to solve this positioning problem with the angular error which results in a nonlinear optimization subproblem with the inconsistent system of constraints.
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