The paper focuses on the convergence rate of the augmented Lagrangian method for nonlinear second-order cone optimization problems. Under a set of assumptions of sufficient conditions, including the componentwise strict complementarity condition, the constraint nondegeneracy condition and the second order sufficient condition, we first study some properties of the augmented Lagrangian and then ...

We consider a class of constrained optimization problems where the objective function is a sum of a smooth function and a nonconvex non-Lipschitz function. Many problems in sparse portfolio selection, edge preserving image restoration and signal processing can be modelled in this form. First we propose the concept of the Karush-Kuhn-Tucker (KKT) stationary condition for the non-Lipschitz proble...

In this paper, a bi-objective model is proposed for designing a pre-positioning network of pharmaceutical supplies considering their limited shelf-life. The presented model aims to consider both cost efficiency and responsiveness by minimization of total cost and the maximum amount of unmet demand under uncertainties in demand and supply sides’ data. Moreover, for effective distribution of reli...

The redundancy allocation problem (RAP) has been studied for many different system structures, objective functions, and distribution assumptions. In this paper, we present a problem formulation and a solution methodology to maximize the system steady-state availability and minimize the system cost for the repairable series-parallel system designs. In the proposed approach, the components’ time-...

Recently a novel reinforcement learning algorithm called event-learning or E-learning was introduced. The algorithm based on events, which are defined as ordered pairs of states. In this setting, the agent optimizes the selection of desired sub-goals by a traditional value-policy function iteration, and utilizes a separated algorithm called the controller to achieve these goals. The advantage o...

Kleinberg [17] proposed in 2000 the first random graph model achieving to reproduce small world navigability, i.e. the ability to greedily discover polylogarithmic routes between any pair of nodes in a graph, with only a partial knowledge of distances. Following this seminal work, a major challenge was to extend this model to larger classes of graphs than regular meshes, introducing the concept...

Multi-objective combinatorial optimization (MOCO) problems, apart from being notoriously difficult and complex to solve in reasonable computational time, they also exhibit high levels of instability in their results in case of uncertainty, which often deviate far from optimality. In this work we propose an integrated methodology to measure and analyze the robustness of MOCO problems, and more s...

We present an algorithm that achieves superlinear convergence for nonlinear programs satisfying the Mangasarian-Fromovitz constraint qualiication and the quadratic growth condition. This convergence result is obtained despite the potential lack of a locally convex augmented Lagrangian. The algorithm solves a succession of subproblems that have quadratic objective and quadratic constraints, both...

1. Abstract A novel strategy for handling the molding constraint for cast parts is presented. In a first step, a simple projection method for the velocity field is applied. If the optimized shape violates thickness constraints, this projection method is no longer sufficient and a general molding constraint is applied at the same time with thickness control. We apply an augmented Lagrangian meth...