Disjunctive cutting planes can tighten a relaxation of a mixed-integer linear program. Traditionally, such cuts are obtained by solving a higher-dimensional linear program, whose additional variables cause the procedure to be computationally prohibitive. Adopting a V-polyhedral perspective is a practical alternative that enables the separation of disjunctive cuts via a linear program with only as … Read more
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is tractable to evaluate constraint function and derivative values in each iteration, but it is intractable to evaluate the objective function or … Read more
This thesis studies derivative-free optimization (DFO), particularly model-based methods and software. These methods are motivated by optimization problems for which it is impossible or prohibitively expensive to access the first-order information of the objective function and possibly the constraint functions. In particular, this thesis presents PDFO, a package we develop to provide both MATLAB and Python … Read more
The late Professor M. J. D. Powell devised five trust-region derivative-free optimization methods, namely COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA. He also carefully implemented them into publicly available solvers, which are renowned for their robustness and efficiency. However, the solvers were implemented in Fortran 77 and hence may not be easily accessible to some users. … Read more
We study the inefficiency of pure Nash equilibria in symmetric unweighted network congestion games. We first explore the impact of symmetry on the worst-case PoA of network congestion games. For polynomial delay functions with highest degree p, we construct a family of symmetric congestion games over arbitrary networks which achieves the same worst-case PoA of … Read more
This paper demonstrates the optimality of an interpolation set employed in derivative-free trust-region methods. This set is optimal in the sense that it minimizes the constant of well-poisedness in a ball centred at the starting point. It is chosen as the default initial interpolation set by many derivative-free trust-region methods based on underdetermined quadratic interpolation, … Read more
Over the last fewyears, the efficient design of processes in hospitals and medical facilities has received more and more attention, particularly when the improvement of the processes is aimed at relieving theworkload of medical staff. To this end,we have developed a method to determine optimal allocations of intra-hospital transports to hospital transport employees. When optimizing … Read more
Cut-strengthening techniques have a significant impact on the computational effectiveness of the Logic-based Benders’ decomposition (LBBD) scheme. While there have been numerous cut-strengthening techniques proposed, very little is understood about which techniques achieve the best computational performance for the LBBD scheme. This is typically due to implementations of LBBD being problem specific and thus, no … Read more
In low-rank matrix recovery, the goal is to recover a low-rank matrix, given a limited number of linear and possibly noisy measurements. Low-rank matrix recovery is typically solved via a nonconvex method called Burer-Monteiro factorization (BM). If the rank of the ground truth is known, BM is free of sub-optimal local solutions, and its true solutions … Read more
\(\) A second-order algorithm is proposed for minimizing smooth nonconvex functions that alternates between regularized Newton and negative curvature steps. In most cases, the Hessian matrix is regularized with the square root of the current gradient and an additional term taking moderate negative curvature into account, a negative curvature step being taken only exceptionnally. As … Read more