Relation between the constant rank and the relaxed constant rank constraint qualifications

This article discusses a relation between the constant rank constraint qualification (CRCQ) and the recently proposed relaxed constant rank constraint qualification (RCRCQ). We show that a parametric constraint system satisfying the RCRCQ is locally diffeomorphic to a system satisfying the CRCQ. We use this result to extend some existing results for the CRCQ to the RCRCQ, establish a relation between the RCRCQ and the Mangasarian–Fromovitz constraint qualification, and obtain a weakened version of the Aubin property under the RCRCQ.     

Some kind of Pareto stationarity for multiobjective problems with equilibrium constraints

ABSTRACT

In this paper, we derive some optimality and stationarity conditions for a multiobjective problem with equilibrium constraints (MOPEC). In particular, under a generalized Guignard constraint qualification, we show that any locally Pareto optimal solution of MOPEC must satisfy the strong Pareto Kuhn-Tucker optimality conditions. We also prove that the generalized Guignard constraint qualification is the weakest constraint qualification for the strong Pareto Kuhn-Tucker optimality. Furthermore, under certain convexity or generalized convexity assumptions, we show that the strong Pareto Kuhn-Tucker optimality conditions are also sufficient for several popular locally Pareto-type optimality conditions for MOPEC.     

一种估计精度限制下的加速退化试验最优设计

讨论了一类步进应力的加速退化试验,在试验假定下,以退化失效分布平均寿命的极大似然估计与其真值的接近程度为标准得到一个精度限制．然后根据试验的过程得到了试验成本函数的一般表达形式．在估计精度的限制之下,最小化成本函数,以此得出试验的最优设计模型．最后,给出了一个数值例子,展示了优化设计的过程．     

A numerical study of crack tip constraint in ductile single crystals

In this work, the effect of crack tip constraint on near-tip stress and deformation fields in a ductile FCC single crystal is studied under mode I, plane strain conditions. To this end, modified boundary layer simulations within crystal plasticity framework are performed, neglecting elastic anisotropy. The first and second terms of the isotropic elastic crack tip field, which are governed by the stress intensity factor K and T-stress, are prescribed as remote boundary conditions and solutions pertaining to different levels of T-stress are generated. It is found that the near-tip deformation field, especially, the development of kink or slip shear bands, is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the crack tip are also strongly influenced by the level of T-stress, with progressive loss of crack tip constraint occurring as T-stress becomes more negative. A family of near-tip fields is obtained which are characterized by two terms (such as K and T or J and a constraint parameter Q) as in isotropic plastic solids.     

A novel finite element model for helical springs

A general and accurate finite element model for helical springs subject to axial loads (extension or/and torsion) is developed in this paper. Due to the establishment of precise boundary conditions, only a slice of the wire cross-section needs to be modelled; hence, more accurate results can be achieved. An example application to a circular cross-sectional spring is analysed in detail.     

MPCC: on necessary conditions for the strong stability of C-stationary points

ABSTRACT

We consider the concept of strongly stable C-stationary points for mathematical programs with complementarity constraints. The original concept of strong stability was introduced by Kojima for standard optimization programs. Adapted to our context, it refers to the local existence and uniqueness of a C-stationary point for each sufficiently small perturbed problem. The goal of this paper is to discuss a Mangasarian-Fromovitz-type constraint qualification and, mainly, provide two conditions which are necessary for strong stability; one is another constraint qualification and the second one refers to bounds on the number of active constraints at the point under consideration.     

On uniqueness of Kuhn-Tucker multipliers in nonlinear programming

Recently Fujiwara, Han and Mangasarian introduced a new constraint qualification which is a slight tightening of the well-known Mangasarian—Fromovitz constraint qualification. We show that this new qualification is a necessary and sufficient condition for the uniqueness of Kuhn—Tucker multipliers. We also show that it implies the satisfaction of second order necessary optimality conditions at a local minimum.     

Using separable programming to solve the multi-product multiple ex-ante constraint newsvendor problem and extensions

This paper provides an approximating programming technique to solve the multi-product newsvendor model in which product demands are independent and stocking quantities are subject to two or more ex-ante linear contraints, such as budget or volume constraints. Previous research has attempted to solve this problem with Lagrange relaxation techniques or by limiting the distribution of demand. However, by taking advantage of the separable nature of the problem, a close approximation of the optimal solution can be found using convex separable programming for any demand distribution in the traditional newsvendor model and extensions. Sensitivity analysis of the linear program provides managerial insight into the effects of parameters of the problem on the optimal solution and future decisions.     

Hybrid Approach with Active Set Identification for Mathematical Programs with Complementarity Constraints

We consider a mathematical program with complementarity constraints (MPCC). Our purpose is to develop methods that enable us to compute a solution or a point with some kind of stationarity to MPCC by solving a finite number of nonlinear programs. We apply an active set identification technique to a smoothing continuation method (Ref. 1) and propose a hybrid algorithm for solving MPCC. We develop also two modifications: one makes use of an index addition strategy; the other adopts an index subtraction strategy. We show that, under reasonable assumptions, all the proposed algorithms possess a finite termination property. Further discussions and numerical experience are given as well This work was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education, Science, Sports, and Culture of Japan. The authors are grateful to Professor Paul Tseng for helpful suggestions on an earlier version of the paper.     

Integrating operations research in constraint programming

This paper presents constraint programming (CP) as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of propagation and tailored algorithms for global constraints. It also allows linear programming to be combined with propagation and novel and varied search techniques which can be easily expressed in CP. The paper describes how CP can be used to exploit linear programming within different kinds of hybrid algorithm. In particular it can enhance techniques such as Lagrangian relaxation, Benders decomposition and column generation.