Design and implementation of a modular interior-point solver for linear optimization

This paper introduces the algorithmic design and implementation of Tulip, an open-source interior-point solver for linear optimization. It implements a regularized homogeneous interior-point algorithm with multiple centrality corrections, and therefore handles unbounded and infeasible problems. The solver is written in Julia, thus allowing for a flexible and efficient implementation: Tulip's algorithmic framework is fully disentangled from linear algebra implementations and from a model's arithmetic. In particular, this allows to seamlessly integrate specialized routines for structured problems. Extensive computational results are reported. We find that Tulip is competitive with open-source interior-point solvers on the H. Mittelmann's benchmark of barrier linear programming solvers. Furthermore, we design specialized linear algebra routines for structured master problems in the context of Dantzig-Wolfe decomposition. These routines yield a tenfold speedup on large and dense instances that arise in power systems operation and two-stage stochastic programming, thereby outperforming state-of-the-art commercial interior point method solvers. Finally, we illustrate Tulip's ability to use different levels of arithmetic precision by solving problems in extended precision

A Decentralized Framework for the Optimal Coordination of Distributed Energy Resources

Demand-response aggregators are faced with the challenge of how to best manage numerous and heterogeneous distributed energy resources (DERs). This paper proposes a decentralized methodology for optimal coordination of DERs. The proposed approach is based on Dantzig-Wolfe decomposition and column generation, thus allowing to integrate any type of resource whose operation can be formulated within a mixed-integer linear program. We show that the proposed framework offers the same guarantees of optimality as a centralized formulation, with the added benefits of distributed computation, enhanced privacy, and higher robustness to changes in the problem data. The practical efficiency of the algorithm is demonstrated through extensive computational experiments, on a set of instances generated using data from Ontario energy markets. The proposed approach was able to solve all test instances to proven optimality, while achieving significant speed-ups over a centralized formulation solved by state-of-the-art optimization software

Separate and combined analysis of successive dependent outcomes after breast-conservation surgery: recurrence, metastases, second cancer and death

<p>Abstract</p> <p>Background</p> <p>In the setting of recurrent events, research studies commonly count only the first occurrence of an outcome in a subject. However this approach does not correctly reflect the natural history of the disease. The objective is to jointly identify prognostic factors associated with locoregional recurrences (LRR), contralateral breast cancer, distant metastases (DM), other primary cancer than breast and breast cancer death and to evaluate the correlation between these events.</p> <p>Methods</p> <p>Patients (n = 919) with a primary invasive breast cancer and treated in a cancer center in South-Western France with breast-conserving surgery from 1990 to 1994 and followed up to January 2006 were included. Several types of non-independent events could be observed for the same patient: a LRR, a contralateral breast cancer, DM, other primary cancer than breast and breast cancer death. Data were analyzed separately and together using a random-effects survival model.</p> <p>Results</p> <p>LRR represent the most frequent type of first failure (14.6%). The risk of any event is higher for young women (less than 40 years old) and in the first 10 years of follow-up after the surgery. In the combined analysis histological tumor size, grade, number of positive nodes, progesterone receptor status and treatment combination are prognostic factors of any event. The results show a significant dependence between these events with a successively increasing risk of a new event after the first and second event. The risk of developing a new failure is greatly increased (RR = 4.25; 95%CI: 2.51-7.21) after developing a LRR, but also after developing DM (RR = 3.94; 95%CI: 2.23-6.96) as compared to patients who did not develop a first event.</p> <p>Conclusion</p> <p>We illustrated that the random effects survival model is a more satisfactory method to evaluate the natural history of a disease with multiple type of events.</p

Fractionation of grape anthocyanin classes using multilayer coil countercurrent chromatography with step gradient elution

Copyright © 2004 American Chemical SocietyStéphane Vidal, Yoji Hayasaka, Emmanuelle Meudec, Véronique Cheynier, and George Skouroumouni