09:45 AM - 10:10 AM
Direct Search Algorithms for solving optimization models with equality constraints
Well known Direct Search Algorithms (DSA) for solving optimization models have been suggested in the open literature; however, only in the last two years DSA that solve a model with equality constraints have appeared. This talk reviews several approaches for solving models with equality constraints:
a) Linear equalities are active additional variables at all iterations of the algorithm.
b) Linear (and nonlinear) equalities constraints are:
b1) transformed to inequalities with a trivial change to the objective function, or
b2) a penalization to the objective function.
Numerical experiments are reported to show the benefits –and shortcomings- of the different approaches.
This work has been funded by the Galician Government under grants ED341D R2016/012.
10:10 AM - 10:35 AM
Multi-fidelity optimization with computationally expensive black-box functions
We discuss our most recent algorithm developments in derivative-free multi-fidelity optimization where both fidelity models are black-box simulations. The low-fidelity function evaluates faster than the high-fidelity function, but may still require several minutes per evaluation. We use the low-fidelity information to decide where the high-fidelity function should be evaluated. This reduces the number of expensive high-fidelity evaluations we have to do for finding the optimum. We develop sampling strategies that rely on local rather than global correlations for making sampling decisions.