Distributionally Robust Optimization: A review on theory and applications

<p style='text-indent:20px;'>In this paper, we survey the primary research on the theory and applications of distributionally robust optimization (DRO). We start with reviewing the modeling power and computational attractiveness of DRO approaches, induced by the ambiguity sets structure and tractable robust counterpart reformulations. Next, we summarize the efficient solution methods, out-of-sample performance guarantee, and convergence analysis. Then, we illustrate some applications of DRO in machine learning and operations research, and finally, we discuss the future research directions.</p>

Understanding the Performance Guarantee of Physical Topology Design for Optical Circuit Switched Data Centers

As a first step of designing O ptical-circuit-switched D ata C enters (ODC), physical topology design is critical as it determines the scalability and the performance limit of the entire ODC. However, prior works on ODC have not yet paid much attention to physical topology design, and the adopted physical topologies either scale poorly, or lack performance guarantee. We offer a mathematical foundation for the design and performance analysis of ODC physical topologies in this paper. We introduce a new performance metric β(G ) to evaluate the gap between a physical topology G and the ideal physical topology. We develop a coupling technique that bypasses a significant amount of computational complexity of calculating β(G). Using β(G ) and the coupling technique, we study four physical topologies that are representative of those in literature, analyze their scalabilities and prove their performance guarantees. Our analysis may provide new guidance for network operators to design better physical topologies for their ODCs.

Approximation Algorithms for the Bottleneck Asymmetric Traveling Salesman Problem

We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem . Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximum-length edge) cost. We achieve an O (log n / log log n ) approximation performance guarantee by giving a novel algorithmic technique to shortcut Eulerian circuits while bounding the lengths of the shortcuts needed. This allows us to build on a related result of Asadpour, Goemans, Mądry, Oveis Gharan, and Saberi to obtain this guarantee. Furthermore, we show how our technique yields stronger approximation bounds in some cases, such as the bounded orientable genus case studied by Oveis Gharan and Saberi. We also explore the possibility of further improvement upon our main result through a comparison to the symmetric counterpart of the problem.

STRICT CONFORMITY OF DOCUMENTS UNDER A PERFORMANCE GUARANTEE. DOES A SIGNED COPY OF A DOCUMENT QUALIFY AS AN ORIGINAL? Stefanutti & Bressan (Pty) Ltd v Nedbank Ltd (unreported judgment delivered on 30 July 2008) (case no 5311/2008) (D&CLD)

Unlike in many overseas jurisdictions, there is a paucity of South African reported case law dealing with certain instruments of payment and guarantees for payment such as documentary letters of credit and performance guarantees, to mention but two examples of instruments prevalent in the field of payment and financing. For this reason any new case law dealing with either letters of credit or performance guarantees is to be welcomed as it would hopefully not only contribute to our understanding of this area of the law, but also provide an opportunity for comment and reflection. This holds especially true since the International Chamber of Commerce has recently (in July 2007) accepted and introduced a new version of the Uniform Customs and Practices for Documentary Credits (hereinafter “the UCP”): UCP 600. In passing: Apart from the main distinction between direct (three-party) and indirect (four-party) demand guarantees, they (ie, demand guarantees) may also be classified by reference to the phase or part of performance theyare designed to secure, hence the following classification of the different types of demand guarantees: tender guarantee (tender bond); performance guarantee (performance bond); advance payment guarantee (repayment guarantee); retention guarantee; and maintenance guarantee (warranty guarantee). In what follows below the author will use the concept of “guarantee”, being a genericterm, when referring to demand and/or performance guarantees in general. The recent decision in Stefanutti & Bressan (Pty) Ltd v Nedbank Ltd (unreported judgment delivered on 30 July 2008 (case no 5311/2008) by the Durban & Coast Local Division of the High Court (now: KwaZulu-Natal High Court, Durban) is a rare and welcome addition to the rather modest collection of South African decisions dealing with performance guarantees.