Solving bilevel programs based on lower-level Mond-Weir duality

This paper focuses on developing effective algorithms for solving bilevel program. The most popular approach is to replace the lower-level problem by its Karush-Kuhn-Tucker conditions to generate a mathematical program with complementarity constraints (MPCC). However, MPCC does not satisfy the Mangasarian-Fromovitz constraint qualification (MFCQ) at any feasible point. In this paper, inspired by a recent work using the lower-level Wolfe duality (WDP), we apply the lower-level Mond-Weir duality to present a new reformulation, called MDP, for bilevel program. It is shown that, under mild assumptions, they are equivalent in globally or locally optimal sense. An example is given to show that, different from MPCC, MDP may satisfy the MFCQ at its feasible points. Relations among MDP, WDP, and MPCC are investigated. Furthermore, in order to compare the new MDP approach with the MPCC and WDP approaches, we design a procedure to generate 150 tested problems randomly and comprehensive numerical experiments showed that MDP has evident advantages over MPCC and WDP in terms of feasibility to the original bilevel programs, success efficiency, and average CPU time.Comment: arXiv admin note: text overlap with arXiv:2302.0683

Stochastic mathematical programs with hybrid equilibrium constraints

AbstractThis paper considers a stochastic mathematical program with hybrid equilibrium constraints (SMPHEC), which includes either “here-and-now” or “wait-and-see” type complementarity constraints. An example is given to describe the necessity to study SMPHEC. In order to solve the problem, the sampling average approximation techniques are employed to approximate the expectations and smoothing and penalty techniques are used to deal with the complementarity constraints. Limiting behaviors of the proposed approach are discussed. Preliminary numerical experiments show that the proposed approach is applicable

Service selection strategic analysis for selfoperated e-commerce platforms under settlement

In order to study whether e-commerce platforms carry out service cooperation after settlement in-depth, this paper focuses on service selection strategic analysis for agent channels on some self-operated e-commerce platforms settled in hybrid e-commerce platforms. We present multi-leader-follower models in two different scenarios with the platforms as leaders and the manufacturers as followers and give some numerical experiments to analyze the impacts of service selection strategies for self-operated platforms on all supply chain members. Our finding shows that if the service cost efficiency is moderate or low, the self-operated platform prefers to provide its service for the agent; otherwise, its selection mainly depends on the unit product service fee. In addition, fierce service competition and high unit service fee are unfavorable to all members, while high service cost efficiency may hurt both the platform and the manufacturer

A novel approach for bilevel programs based on Wolfe duality

This paper considers a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most popular approach is to replace the lower-level program by its KKT conditions and then the bilevel program can be reformulated as a mathematical program with equilibrium constraints (MPEC for short). However, since the MPEC does not satisfy the Mangasarian-Fromovitz constraint qualification at any feasible point, the well-developed nonlinear programming theory cannot be applied to MPECs directly. In this paper, we apply the Wolfe duality to show that, under very mild conditions, the bilevel program is equivalent to a new single-level reformulation (WDP for short) in the globally and locally optimal sense. We give an example to show that, unlike the MPEC reformulation, WDP may satisfy the Mangasarian-Fromovitz constraint qualification at its feasible points. We give some properties of the WDP reformulation and the relations between the WDP and MPEC reformulations. We further propose a relaxation method for solving WDP and investigate its limiting behavior. Comprehensive numerical experiments indicate that, although solving WDP directly does not perform very well in our tests, the relaxation method based on the WDP reformulation is quite efficient

Dimethyl 3,5-diethyl-1H-pyrrole-2,4-dicarboxyl­ate

The title pyrrole derivative, C12H17NO4, consists of a pyrrole ring with two diagonally attached meth­oxy­carbonyl groups and two diagonally attached ethyl groups. The two carbonyl groups are approximately in the same plane as the pyrrole ring, making dihedral angles of 3.50 (19) and 6.70 (19)°. In the crystal, adjacent mol­ecules are assembled into dimers in a head-to-head mode by pairs of inter­molecular N—H⋯O hydrogen bonds

Bis(2-amino­pyridine-κN 1)bis­(benzoato-κO)cobalt(II)

In the title compound, [Co(C7H5O2)2(C5H6N2)2], the CoII atom is hexa­coordinated by four O atoms from two benzoate anions, and two N atoms from two 2-amino­pyridine mol­ecules, resulting in a distorted octa­hedral geometry. Both benzoate anions act as bidentate ligands and both 2-amino­pyridine mol­ecules are coordinated to the metal through their pyridyl N atoms. The crystal packing is stabilized by inter­molecular N—H⋯O hydrogen bonds, C—H⋯π, and π–π stacking inter­actions involving benzoate anions and 2-amino­pyridine mol­ecules

Novel insights into bacterial dimethylsulfoniopropionate catabolism in the East China Sea

The compatible solute Dimethylsulfoniopropionate (DMSP), made by many marine organisms, is one of Earth’s most abundant organosulfur molecules. Many marine bacteria import DMSP and can degrade it as a source of carbon and/or sulfur via DMSP cleavage or DMSP demethylation pathways, which can generate the climate active gases dimethyl sulfide (DMS) or methanthiol (MeSH), respectively. Here we used culture-dependent and -independent methods to study bacteria catabolising DMSP in East China Sea (ECS). Of bacterial isolates, 42.11% showed DMSP-dependent DMS (Ddd+) activity, and 12.28% produced detectable levels of MeSH. Interestingly, although most Ddd+ isolates were Alphaproteobacteria (mainly Roseobacters), many gram-positive Actinobacteria were also shown to cleave DMSP producing DMS. The mechanism by which these Actinobacteria cleave DMSP is unknown, since no known functional ddd genes have been identified in genome sequences of Ddd+ Microbacterium and Agrococcus isolates or in any other sequenced Actinobacteria genomes. Gene probes to the DMSP demethylation gene dmdA and the DMSP lyase gene dddP demonstrated that these DMSP-degrading genes are abundant and widely distributed in ECS seawaters. dmdA was present in relatively high proportions in both surface (19.53% ± 6.70%) and bottom seawater bacteria (16.00% ± 8.73%). In contrast, dddP abundance positively correlated with chlorophyll a, and gradually decreased with the distance from land, which implies that the bacterial DMSP lyase gene dddP might be from bacterial groups that closely associate with phytoplankton. Bacterial community analysis showed positive correlations between Rhodobacteraceae abundance and concentrations of DMS and DMSP, further confirming the link between this abundant bacterial class and the environmental DMSP cycling

Limonoids and triterpenoids from the twigs and leaves of Dysoxylum hainanense

Four new limonoids, dysohainanins A–D (1–4), and two new triterpenoids, dysohainanins E and F (5 and 6), together with seven known ones were isolated from the twigs and leaves of Dysoxylum hainanense Merr. The structures of the new compounds were determined by a variety of spectroscopic methods. The cytotoxic activities of these compounds were evaluated, and the known compound ent-19-nor-4,16,18-trihydroxy-8(14)-pomaren-15-one (13) showed in vitro cytotoxicity against HL-60, A-549, MCF-7, and SW480 cells, with IC(50) values of 24.3, 28.1, 30.7, and 22.5 µM, respectively. Compounds 2 and 3 were tested their insecticidal activities using brine shrimp and both of them were inactive. [Image: see text] ELECTRONIC SUPPLEMENTARY MATERIAL: Supplementary material is available for this article at 10.1007/s13659-011-0030-8 and is accessible for authorized users

Mutation of SLC35D3 causes metabolic syndrome by impairing dopamine signaling in striatal D1 neurons

We thank Dr. Ya-Qin Feng from Shanxi Medical University, Dr. Tian-Yun Gao from Nanjing University and Dr. Yan-Hong Xue from Institute of Biophysics (CAS) for technical assistance in this study. We are very thankful to Drs. Richard T. Swank and Xiao-Jiang Li for their critical reading of this manuscript and invaluable advice. Funding: This work was partially supported by grants from National Basic Research Program of China (2013CB530605; 2014CB942803), from National Natural Science Foundation of China 1230046; 31071252; 81101182) and from Chinese Academy of Sciences (KSCX2-EW-R-05, KJZD-EW-L08). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD