Infeasible-Interior-Point methods shown in previous homeworks are well behaved when the number of constraints are small and the dimension of the energy function domain is also small. This fact is easily seen, since each iteration of such methods requires of solving a linear equation system whose size depends precisely on the number of constraints and the dimension of the search space. In additi...

In this paper, we consider a class of structured nonsmooth difference-of-convex (DC) constrained DC programs in which the first convex component objective and constraints is sum smooth function, their second supremum finitely many functions. The existing methods for problem usually have weak convergence guarantee or require feasible initial point. Inspired by recent work Pang et al. [Pang J-S, ...

We propose an augmented Lagrangian algorithm for solving large-scale constrained optimization problems. The novel feature of the algorithm is an adaptive update for the penalty parameter motivated by recently proposed techniques for exact penalty methods. This adaptive updating scheme greatly improves the overall performance of the algorithm without sacrificing the strengths of the core augment...

We investigate risk-averse stochastic optimization problems where riskaverse preferences are modeled with a stochastic order constraint. We propose augmented Lagrangian methods for the numerical solution of problems with multivariate and univariate stochastic order relations. The methods constructs finite-dimensional approximations of the optimization problem whose solutions converge to the sol...