We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...

The U.S. Department of Agriculture (USDA) currently uses a bidding system to determine carriers and suppliers that would partner in providing food aid annually in response to global emergencies and famine. We mimic the USDA approach via a robust optimization model featuring box and ellipsoid uncertainty frameworks to account for uncertainties in demand, supplier and carrier bid prices. Through ...

Robust explicit/multi-parametric controllers are designed for constrained, linear discrete–time systems with box-constrained states and inputs, involving uncertainty in the left–hand side (LHS) of the Model Predictive Control (MPC) optimization model. Based on previous results, this work presents a new algorithm that features: (i) a dynamic programming reformulation of the MPC optimization, (ii...

This study has been inspired by the paper "An efficient 3D topology optimization code written in MATLAB” written by Liu and Tovar (2014) demonstrating that SIMP-based three-dimensional (3D) topology optimization of continuum structures can be implemented in 169 lines of MATLAB code. Based on the above paper, we show here that, by simple and easy-to-understand modificati...

Many real-world design problems involve optimization of expensive black-box functions. Bayesian (BO) is a promising approach for solving such challenging using probabilistic surrogate models to systematically tradeoff between exploitation and exploration the space. Although BO often applied unconstrained problems, it has recently been extended constrained setting. Current methods, however, cann...

*Correspondence: Oleg N. Kirillov, Magneto-Hydrodynamics Division, Institute of Fluid Dynamics, Helmholtz-Zentrum DresdenRossendorf, PO Box 510119, D-01314 Dresden, Germany e-mail: [email protected] Consider the set of monic fourth-order real polynomials transformed so that the constant term is one. In the three-dimensional space of the coefficients describing this set, the domain of asymptoti...