This work deals with convergence to points satisfying the weak second-order necessary optimality conditions of a second-order safeguarded augmented Lagrangian method from the literature. To this end, we propose a new second-order sequential optimality condition that is, in a certain way, based on the iterates generated by the algorithm itself. This also allows us to … Read more
Mathematical modeling, simulation, and optimization can significantly support the development and characterization of chromatography steps in the biopharmaceutical industry. Particularly mechanistic models become preferably used, as these models, once carefully calibrated, can be employed for a reliable optimization. However, model calibration is a difficult task in this context due to high correlations between parameters, highly … Read more
Considering a standard nonlinear programming problem, one may view a subset of the equality constraints as an embedded Riemannian manifold. In this paper we investigate the differences between the Euclidean and the Riemannian approach for this problem. It is well known that the linear independence constraint qualification for both approaches are equivalent. However, when considering … Read more
Given a nominal combinatorial optimization problem, we consider a robust two-stages variant with polyhedral cost uncertainty, called Decision-Dependent Information Discovery (DDID). In the first stage, DDID selects a subset of uncertain cost coefficients to be observed, and in the second-stage, DDID selects a solution to the nominal problem, where the remaining cost coefficients are still … Read more
It is known that second-order (Studniarski) contingent derivatives can be used to compute tangents to the solution set of a generalized equation when standard (first-order) regularity conditions are absent, but relaxed (second-order) regularity conditions are fulfilled. This fact, roughly speaking, is only relevant in practice as long as the computation of second-order contingent derivatives itself … Read more
We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of four algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss-army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with … Read more
For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called “l0 norm”, which counts the number of non-zero components in a vector, is a strong reliable mechanism of enforcing … Read more
We study a Stackelberg game in which a government positions rapid response teams and thereafter a terrorist attacks a location on a line segment. We assume the damage associated to such an attack to be time dependent. We show that there exists a subgame perfect Nash equilibrium that balances the possible damage on all intervals … Read more
We are excited to present the early release of Part I of our book “Optimizing with Column Generation: advanced Branch-Cut-and-Price Algorithms”. While the book’s ultimate goal, as suggested by its subtitle, is to describe cutting-edge techniques in these algorithms, this objective is primarily addressed in the forthcoming Part II. However, we feel that the completed … Read more
\(\) Peak cost is a novel objective for flows over time that describes the amount of workforce necessary to run a system. We focus on minimising peak costs in the context of maximum temporally repeated flows and formulate the corresponding MPC-MTRF problem. First, we discuss the limitations that emerge when restricting the solution space to … Read more