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We propose an optimization algorithm to compute the optimal sensor locationsin experimental design in the formulation of Bayesian inverse problems, wherethe parameter-to-observable mapping is described through an integral equationand its discretization results in a continuously indexed matrix whose sizedepends on the mesh size n. By approximating the gradient and Hessian of theobjective design criterion from Chebyshev interpolation, we solve a sequence ofquadratic programs and achieve the complexity $\mathcal{O}(n\log^2(n))$. Anerror analysis guarantees the integrality gap shrinks to zero as $n\to\infty$,and we apply the algorithm on a two-dimensional advection-diffusion equation,to determine the LIDAR's optimal sensing directions for data collection.

Solving Optimal Experimental Design with Sequential Quadratic Programming and Chebyshev Interpolation