Given a univariate polynomial, its abscissa is the maximum real part of its roots. The abscissa arises naturally when controlling linear differential equations. As a function of the polynomial coefficients, the abscissa is H\”older continuous, and not locally Lipschitz in general, which is a source of numerical difficulties for designing and optimizing control laws. In … Read more
An algorithm is proposed to optimize the performance of multiphase structures (composites) under elastodynamic loading conditions. The goal is to determine the distribution of material in the structure such that the time-averaged total stored energy of structure is minimized. A penalization strategy is suggested to avoid the checkerboard instability, simultaneously to generate near 0-1 topologies. … Read more
An unconditionally energy stable time stepping scheme is introduced to solve Cahn-Morral-like equations in the present study. It is constructed based on the combination of David Eyre’s time stepping scheme and Schur complement approach. Although the presented method is general and independent to the choice of homogeneous free energy density function term, logarithmic and polynomial … Read more
We study the design of robust truss structures under mechanical equilibrium, displacements and stress constraints. Our main objective is to minimize the total amount of material, for the purpose of finding the most economic structure. A robust design is found by considering load perturbations. The nature of the constraints makes the mathematical program nonconvex. In … Read more
We propose a novel, Bayesian framework for assessing the relative strengths of data-driven ambiguity sets in distributionally robust optimization (DRO). The key idea is to measure the relative size between a candidate ambiguity set and an \emph{asymptotically optimal} set as the amount of data grows large. This asymptotically optimal set is provably the smallest convex … Read more
We consider a combinatorial optimization problem for spatial information cloaking. The problem requires to compute one or several disjoint arborescences on a graph from a predetermined root or subset of candidate roots, so that the number of vertices in the arborescences is minimized but a given threshold on the overall weight associated with the vertices … Read more
We propose an algorithm for solving nonsmooth, nonconvex, constrained optimization problems as well as a new set of visualization tools for comparing the performance of optimization algorithms. Our algorithm is a sequential quadratic optimization method that employs Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton Hessian approximations and an exact penalty function whose parameter is controlled using a steering strategy. … Read more
This paper approximates simulation models by B-splines with a penalty on high-order finite differences of the coefficients of adjacent B-splines. The penalty prevents overfitting. The simulation output is assumed to be nonnegative. The nonnegative spline simulation metamodel is casted as a second-order cone programming model, which can be solved efficiently by modern optimization techniques. The … Read more
The classical SVM is an optimization problem minimizing the hinge losses of mis-classified samples with the regularization term. When the sample size is small or data has noise, it is possible that the classifier obtained with training data may not generalize well to pop- ulation, since the samples may not accurately represent the true population … Read more
An important problem in tree breeding is optimal selection from candidate pedigree members to produce the highest performance in seed orchards, while conserving essential genetic diversity. The most beneficial members should contribute as much as possible, but such selection of orchard parents would reduce performance of the orchard progeny due to serious inbreeding. To avoid … Read more