Quadratic Multipoint Exponential Approximation: Surrogate Model for Large-Scale Optimization

Abstract

Sequential Linear Programming (SLP) is a well-known first-order optimization method. Sequential quadratic programming (SQP) is generally preferred for smooth problems, because it is second-order accurate; however, it suffers from the curse of dimensionality for large numbers of design variables. For large-scale problems, SLP may be a good alternative, although its performance depends on the move-limit strategy, the efficiency of the LP solver, and obviously the nonlinearity of the functions. A robust implementation of SLP with a trust region strategy is implemented here in conjunction with a large-scale LP solver. The number of SLP outer-loop iterations to converge is demonstrated to be reduced by an intermediate variable transformation during the linearization. The well-known two-point exponential approximation (TPEA) is extended to take advantage of more than two previous points in determining intervening variables, which can be beneficial particularly for temporarily inactive variables. A single set of intermediate variables are selected for use with all constraint and objective functions, based on Lagrangian sensitivity, to maintain a linear sub-problem for SLP. Quadratic terms constructed in a reduced sub-space are explored for efficient large-scale SQP.