Airport coordination is a demand control mechanism that maximizes the use of existing infrastructure at congested airports. Aircraft operators submit a list of regular flights that they wish to operate over a five to seven-month period and a designated coordinator is responsible for allocating the available airport slots, which represent the permission to operate a … Read more
Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for high-dimensional optimal stopping that are popular in practice produce deterministic linear policies — policies that deterministically stop based on the … Read more
In this paper, we propose a stochastic Gauss-Newton (SGN) algorithm to study the online principal component analysis (OPCA) problem, which is formulated by using the symmetric low-rank product (SLRP) model for dominant eigenspace calculation. Compared with existing OPCA solvers, SGN is of improved robustness with respect to the varying input data and algorithm parameters. In … Read more
We consider a standard distributed consensus optimization problem where a set of agents connected over an undirected network minimize the sum of their individual (local) strongly convex costs. Alternating Direction Method of Multipliers (ADMM) and Proximal Method of Multipliers (PMM) have been proved to be effective frameworks for design of exact distributed second order methods … Read more
We develop a fully asynchronous proximal bundle method for solving non-smooth, convex optimization problems. The algorithm can be used as a drop-in replacement for classic bundle methods, i.e., the function must be given by a first-order oracle for computing function values and subgradients. The algorithm allows for an arbitrary number of master problem processes computing … Read more
We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy is employed. The proposed algorithm combines an SAA subgradient with the spectral coefficient in order to provide a suitable direction which improves … Read more
In this paper, we propose a filter sequential adaptive regularisation algorithm using cubics (ARC) for solving nonlinear equality constrained optimization. Similar to sequential quadratic programming methods, an ARC subproblem with linearized constraints is considered to obtain a trial step in each iteration. Composite step methods and reduced Hessian methods are employed to tackle the linearized … Read more
The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear solver employed to factorize the Karush–Kuhn–Tucker (KKT) system at each iteration of the algorithm. When solving large-scale nonlinear problems, state-of-the art IPM solvers rely on efficient sparse linear solvers to solve the KKT … Read more
We present a branch-and-prune procedure for discrete Nash equilibrium problems with a convex description of each player’s strategy set. The derived pruning criterion does not require player convexity, but only strict convexity of some player’s objective function in a single variable. If satisfied, it prunes choices for this variable by stating activity of certain constraints. … Read more
Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consist of applying a certain number of steps of gradient or subgradient descent on each single objective at each iteration. In this paper, we show that stochastic alternating … Read more