Global Convergence of Augmented Lagrangian Method Applied to Mathematical Program with Switching Constraints

The mathematical program with switching constraints (MPSC) is a kind of problems with disjunctive constraints. The existing convergence results cannot directly be applied to this kind of problem since the required constraint qualifications for ensuring the convergence are very likely to fail. In this paper, we apply the augmented Lagrangian method (ALM) to solve the … Read more

Rates of convergence of sample average approximation under heavy tailed distributions

In this paper, we consider the rate of convergence with sample average approximation (SAA) under heavy tailed distributions and quantify it under both independent identically distributed (iid) sampling and non-iid sampling. We rst derive the polynomial rate of convergence for random variable under iid sampling. Then, the uniform polynomial rates of convergence for both random … Read more

Distributionally Robust Reward-risk Ratio Programming with Wasserstein Metric

Reward-risk ratio (RR) is a very important stock market definition. In recent years, people extend RR model as distributionally robust reward-risk ratio (DRR) to capture the situation that the investor does not have complete information on the distribution of the underlying uncertainty. In this paper, we study the DRR model where the ambiguity on the … Read more

Optimality conditions of set-valued optimization problem involving relative algebraic interior in ordered linear spaces

In this paper, firstly, a generalized subconvexlike set-valued map involving the relative algebraic interior is introduced in ordered linear spaces. Secondly, some properties of a generalized subconvexlike set-valued map are investigated. Finally, the optimality conditions of set-valued optimization problem are established. Citation {\bf AMS 2010 Subject Classifications:} 90C26, 90C29, 90C30 Article Download View Optimality conditions … Read more