### A density result in vector optimization.

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This paper derives a good approach to approximating the expected inventory level per unit time for the continuous review (Q, r) perishable inventory system. Three existing approximation approaches are examined and compared with the proposed approach. Three stockout cases, including the full backorder, the partial backorder, and the full lost sales cases, which customers or material users generally use to respond to a stockout condition are considered. This study reveals the fact that the...

We propose a modified standard embedding for solving the linear complementarity problem (LCP). This embedding is a special one-parametric optimization problem $P\left(t\right),t\in [0,1]$. Under the conditions (A3) (the Mangasarian–Fromovitz Constraint Qualification is satisfied for the feasible set $M\left(t\right)$ depending on the parameter $t$), (A4) ($P\left(t\right)$ is Jongen–Jonker– Twilt regular) and two technical assumptions, (A1) and (A2), there exists a path in the set of stationary points connecting the chosen starting point for $P\left(0\right)$ with a certain...

Embedding approaches can be used for solving non linear programs P. The idea is to define a one-parametric problem such that for some value of the parameter the corresponding problem is equivalent to P. A particular case is the multipliers embedding, where the solutions of the corresponding parametric problem can be interpreted as the points computed by the multipliers method on P. However, in the known cases, either path-following methods can not be applied or the necessary conditions for its convergence...

In this paper, we deal with strong stationarity conditions for mathematical programs with equilibrium constraints (MPEC). The main task in deriving these conditions consists in calculating the Fréchet normal cone to the graph of the solution mapping associated with the underlying generalized equation of the MPEC. We derive an inner approximation to this cone, which is exact under an additional assumption. Even if the latter fails to hold, the inner approximation can be used to check strong stationarity...

Editorial from the Editor-in-Chief regarding this case of plagiarismPhilippe Mahey 1 Introduction Plagiarism is a plague that any scientific publication in any discipline should fight and eradicate all over the world. Unfortunately, if, on the one hand, the powerful search engines available on the web have helped referees to identify most of the cases, the increasing number of publications have on the other hand facilitated that dubious practice and the number of cases have increased. The case...

In this short paper, we are concerned with the stability of nonlinear bilevel programs. A stability problem is proven and an example is given to illustrate this theorem.