In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most prominent theoretical results of RO over the past decade, we will also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we will highlight successful applications of RO across a wide spectrum of domains, including, but not limited to, finance, statistics, learning, and engineering.

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The mammalian abasic endonuclease, APE1, has two distinct roles in the repair of oxidative DNA damage and in gene regulation. Here we show that both functions are essential for cell survival. Deletion of the APE1 gene causes embryonic lethality in mice, and no nullizygous embryo fibroblasts have been isolated. We have now established nullizygous embryo fibroblast lines from APE1 ؊/؊ mouse embryos that are transgenic with the ''floxed'' human APE1 (hAPE1) gene. Removal of hAPE1 by Cre expression through nuclear microinjection elicited apoptosis in these cells within 24 h, which was blocked by coinjection of the wild-type hAPE1 gene. In contrast, mutant hAPE1 alleles, lacking either the DNA repair or acetylation-mediated gene regulatory function, could not prevent apoptosis, although the combination of these two mutants complemented APE deficiency induced by Cre. These results indicate that distinct and separable functions of APE1 are both essential for mammalian cells even in vitro and provide the evidence that mammalian cells, unlike yeast or Escherichia coli, absolutely require APE for survival, presumably to protect against spontaneous oxidative DNA damage.conditional gene inactivation ͉ DNA repair ͉ endogenous DNA damage ͉ base excision repair A basic endonuclease (APE), a ubiquitous enzyme, plays a central role in repairing toxic and mutagenic abasic (AP) sites generated in genomes during the repair of oxidation and alkylation damage through the base excision repair (BER) pathway (1). Oxidative DNA lesions, including AP sites, are also spontaneously generated at an estimated rate of 1.5 ϫ 10 5 residues⅐cell Ϫ1 ⅐day Ϫ1 (2). Unlike two distinct APEs present in Escherichia coli and Saccharomyces cerevisiae, only one active APE, APE1, an ortholog of E. coli xth and yeast APN2, has been identified in mammalian cells (3). Based on sequence homology, a second APE-like gene, APE2, was cloned from mammalian cells. However, we could not detect APE activity in the recombinant human APE2 (4), and hAPE2, unlike hAPE1, could not complement yeast APE mutants (5). Although APE-negative bacteria and yeast are viable, very early death (3.5-7.5 days after fertilization) was observed in APE1 nullizygous mouse embryos (6-8). Unlike other BER proteins, e.g., DNA polymerase ␤ and X-ray cross complementation group 1, which are essential for embryonic survival but not for mouse embryonic fibroblasts (MEFs) cultured in vitro (9, 10), APE1-null MEF mutant lines have not been established. The mammalian APE1, independently identified as redox-enhancing factor 1 (Ref1), has a distinct regulatory function in reductively activating C-Jun, p53, and other transcription factors (3, 11) for which Cys-65 (Cys-64 in mouse APE1) was identified as the active site (12). The N-terminal region of the 36-kDa polypeptide, including Cys-65, is not conserved in the E. coli homolog exonuclease III. An additional regulatory function of APE1͞Ref1 was identified in Ca 2ϩ -dependent down-regulation of the parathyroid hormone and renin genes containing negativ...

We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a "penalty" that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values.