Abstract We study nonlinear optimization problems with a stochastic objective and deterministic equality inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural networks. propose an active-set sequential quadratic programming (StoSQP) algorithm that utilizes differentiable exact augmented Lagrangian as the merit fu...

In practice, due to the lack of information, imprecise variables which come from experts’ empirical data usually appear. In order to deal with these imprecise variables, uncertainty theory is proposed and has been proved to be an efficient method. This paper introduces uncertainty theory into travelling salesman problem (TSP), in which the link travel times are assumed to be uncertain variables...

To address the AC network-constrained unit commitment problem, we propose an effective three-step solution approach. We first solve a DC (mixed-integer linear) approximation of original problem to identify initial and set transmission lines likely be congested. Secondly, with linear as starting point, mixed-integer second-order conic relaxation using active strategy regarding constraints. Final...

The paper is devoted to the study of general nonsmooth problems of cone-constrained optimization (or conic programming) important for various aspects of optimization theory and applications. Based on advanced constructions and techniques of variational analysis and generalized differentiation, we derive new necessary optimality conditions (in both " exact " and " fuzzy " forms) for nonsmooth co...

Project scheduling problem is mainly to determine the schedule of allocating resources in order to balance the total cost and the completion time. This paper chiefly uses chance theory to introduce project scheduling problem with uncertain variables. First, two types of single-objective programming models with uncertain variables as uncertain chance-constrained model and uncertain maximization ...