Best and Worst Optimum for Linear Programs with Interval Right Hand Sides

A New Algorithm for Privacy-Preserving Horizontally Partitioned Linear Programs

Journal of Mathematics ◽

10.1155/2021/6651480 ◽

2021 ◽

Vol 2021 ◽

pp. 1-4

Author(s):

Chengxue Zhang ◽

Debin Kong ◽

Peng Pan ◽

Mingyuan Zhou

Keyword(s):

Linear Programming ◽

Random Matrix ◽

Optimal Solution ◽

Full Rank ◽

Linear Programs ◽

Program Problem ◽

Constraint Matrix ◽

Right Hand ◽

Linear Program Problem ◽

The Matrix

In a linear programming for horizontally partitioned data, the equality constraint matrix is divided into groups of rows. Each group of the matrix rows and the corresponding right-hand side vector are owned by different entities, and these entities are reluctant to disclose their own groups of rows or right-hand side vectors. To calculate the optimal solution for the linear programming in this case, Mangasarian used a random matrix of full rank with probability 1, but an event with probability 1 is not a certain event, so a random matrix of full rank with probability 1 does not certainly happen. In this way, the solution of the original linear programming is not equal to the solution of the secure linear programming. We used an invertible random matrix for this shortcoming. The invertible random matrix converted the original linear programming problem to a secure linear program problem. This secure linear programming will not reveal any of the privately held data.

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Characterization of facets for multiple right-hand choice linear programs

Mathematical Programming Studies - Mathematical Programming at Oberwolfach ◽

10.1007/bfb0120925 ◽

1981 ◽

pp. 112-142 ◽

Cited By ~ 20

Author(s):

Ellis L. Johnson

Keyword(s):

Linear Programs ◽

Right Hand

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Solving linear programs with multiple right-hand sides: Pricing and ordering schemes

Annals of Operations Research ◽

10.1007/bf02187648 ◽

1996 ◽

Vol 64 (1) ◽

pp. 237-259 ◽

Cited By ~ 4

Author(s):

Horand I. Gassmann ◽

Stein W. Wallace

Keyword(s):

Linear Programs ◽

Right Hand ◽

Ordering Schemes

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Editorial Note

Journal of Speech Disorders ◽

10.1044/jshd.1101.02 ◽

1946 ◽

Vol 11 (1) ◽

pp. 2-2

Keyword(s):

Editorial Note ◽

Speech Sounds ◽

Left Hand ◽

Hand Column ◽

Right Hand ◽

Infant Speech ◽

The Right

In the article “Infant Speech Sounds and Intelligence” by Orvis C. Irwin and Han Piao Chen, in the December 1945 issue of the Journal, the paragraph which begins at the bottom of the left hand column on page 295 should have been placed immediately below the first paragraph at the top of the right hand column on page 296. To the authors we express our sincere apologies.

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Eosinophilic vasculitis: an inhabitual and resistant manifestation of a vasculitis

VASA ◽

10.1024/0301-1526/a000060 ◽

2010 ◽

Vol 39 (4) ◽

pp. 344-348 ◽

Cited By ~ 3

Author(s):

Jandus ◽

Bianda ◽

Alerci ◽

Gallino ◽

Marone

Keyword(s):

Skin Biopsy ◽

Intravenous Iron ◽

Small Vessel Vasculitis ◽

High Dose ◽

Raynaud Phenomenon ◽

The Third ◽

Left Elbow ◽

Right Hand ◽

The Right ◽

Trunk Skin

A 55-year-old woman was referred because of diffuse pruritic erythematous lesions and an ischemic process of the third finger of her right hand. She was known to have anaemia secondary to hypermenorrhea. She presented six months before admission with a cutaneous infiltration on the left cubital cavity after a paravenous leakage of intravenous iron substitution. She then reported a progressive pruritic erythematous swelling of her left arm and lower extremities and trunk. Skin biopsy of a lesion on the right leg revealed a fibrillar, small-vessel vasculitis containing many eosinophils.Two months later she reported Raynaud symptoms in both hands, with a persistent violaceous coloration of the skin and cold sensation of her third digit of the right hand. A round 1.5 cm well-delimited swelling on the medial site of the left elbow was noted. The third digit of her right hand was cold and of violet colour. Eosinophilia (19 % of total leucocytes) was present. Doppler-duplex arterial examination of the upper extremities showed an occlusion of the cubital artery down to the palmar arcade on the right arm. Selective angiography of the right subclavian and brachial arteries showed diffuse alteration of the blood flow in the cubital artery and hand, with fine collateral circulation in the carpal region. Neither secondary causes of hypereosinophilia nor a myeloproliferative process was found. Considering the skin biopsy results and having excluded other causes of eosinophilia, we assumed the diagnosis of an eosinophilic vasculitis. Treatment with tacrolimus and high dose steroids was started, the latter tapered within 12 months and then stopped, but a dramatic flare-up of the vasculitis with Raynaud phenomenon occurred. A new immunosupressive approach with steroids and methotrexate was then introduced. This case of aggressive eosinophilic vasculitis is difficult to classify into the usual forms of vasculitis and constitutes a therapeutic challenge given the resistance to current immunosuppressive regimens.

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