4 research outputs found
Optimization for L1-Norm Error Fitting via Data Aggregation
We propose a data aggregation-based algorithm with monotonic convergence to a
global optimum for a generalized version of the L1-norm error fitting model
with an assumption of the fitting function. The proposed algorithm generalizes
the recent algorithm in the literature, aggregate and iterative disaggregate
(AID), which selectively solves three specific L1-norm error fitting problems.
With the proposed algorithm, any L1-norm error fitting model can be solved
optimally if it follows the form of the L1-norm error fitting problem and if
the fitting function satisfies the assumption. The proposed algorithm can also
solve multi-dimensional fitting problems with arbitrary constraints on the
fitting coefficients matrix. The generalized problem includes popular models
such as regression and the orthogonal Procrustes problem. The results of the
computational experiment show that the proposed algorithms are faster than the
state-of-the-art benchmarks for L1-norm regression subset selection and L1-norm
regression over a sphere. Further, the relative performance of the proposed
algorithm improves as data size increases
Efficient solution selection for two-stage stochastic programs
Sampling-based stochastic programs are extensively applied in practice. However, the resulting models tend to be computationally challenging. A reasonable number of samples needs to be identified to represent the random data, and a group of approximate models can then be constructed using such a number of samples. These approximate models can produce a set of potential solutions for the original model. In this paper, we consider the problem of allocating a finite computational budget among numerous potential solutions of a two-stage linear stochastic program, which aims to identify the best solution among potential ones by conducting simulation under a given computational budget. We propose a two-stage heuristic approach to solve the computational resource allocation problem. First, we utilise a Wasserstein-based screening rule to remove potentially inferior solutions from the simulation. Next, we use a ranking and selection technique to efficiently collect performance information of the remaining solutions. The performance of our approach is demonstrated through well-known benchmark problems. Results show that our method provides good trade-offs between computational effort and solution performance