A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear-equality-constrained optimization problems in which the objective function is defined by an expectation. The algorithmic structure of the proposed method is based on a step decomposition strategy that is known in the literature to be widely effective in practice, wherein each search direction is computed as the sum of a normal step (toward linearized feasibility) and a tangential step (toward objective decrease in the null space of the constraint Jacobian). However, the proposed method is unique from others in the literature in that it both allows the use of stochastic objective gradient estimates and possesses convergence guarantees even in the setting in which the constraint Jacobians may be rank-deficient. The results of numerical experiments demonstrate that the algorithm offers superior performance when compared with popular alternatives.
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Effective optimization using sample persistence: A case study on quantum annealers and various Monte Carlo optimization methods
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The problem of air-to-surface trajectory optimization for a low-altitude skid-to-turn vehicle is considered. The objective is for the vehicle to move level at a low altitude for as long as possible and perform a rapid bunt (negative sensed-acceleration load) maneuver near the final time in order to attain terminal target conditions. The vehicle is modeled as a point mass in motion over a flat Earth, and the vehicle is controlled using thrust magnitude, angle of attack, and sideslip angle. The trajectory optimization problem is posed as a two-phase optimal control problem using a weighted objective function. The work described in this paper is the first part of a two-part sequence on trajectory optimization and guidance of a skid-to-turn vehicle. In both cases, the objective is to minimize the time taken by the vehicle to complete a bunt maneuver subject to the following constraints: dynamic, boundary, state, path, and interior-point event constraints. In the first part of this two-part study, the performance of thevehicle is assessed. In particular, the key features of the optimal reference trajectories and controls are provided. The results of this study identify that as greater weight is placed on minimizing the height of the bunt maneuver or as the maximum altitude constraint is raised, the time of the bunt maneuver decreases and the time of the problem solution increases. Also, the results of this study identify that as the allowable crossrange of the vehicle is reduced, the time and height of the bunt maneuver increases and the time of the problem solution decreasemore » « less
