Measures of risk appear in two categories: Risk capital measures serve to determine the necessary amount of risk capital in order to avoid ruin if the outcomes of an economic activity are uncertain and their negative values may be interpreted as acceptability measures (safety measures). Pure risk measures (risk deviation measures) are natural generalizations of the standard deviation. While pur...

K. Larsen, M. Soner, and G. Zitkovic kindly pointed out to us an error in our paper [1] which appeared in 2001 in this journal. They also provide an explicit counter-example in [4]. In Theorem 3.1 of [1] it was incorrectly claimed (among several other correct assertions) that the value function u(x) is continuously differentiable. The erroneous argument for this assertion is contained in Remark...

We consider the piecewise linear approximation of a concave function representing the value function of a parameterized convex program. Using dynamic programming, we derive a procedure for selecting the knots at which an oracle provides the function value and one supergradient. The procedure is adaptive in that the choice of a knot is dependent on the choice of the previous knots. It is also op...

Code division multiple access (CDMA) networks allow subscribers to share frequencies, so optimizing revenue involves reserving channel equivalents to each market subject to signal-tointerference constraints at the radio towers. We present a yield management model inspired by those from the airline industry to optimize revenue under uncertainty. We describe the optimality conditions and develop ...

Our objectives are a) To describe the detailed structure of the air flow in a mature hurricane, b) To understand the vertical force balance in the eye and the eyewall, c) To investigate the presence of supergradient flow in hurricanes and the underlying processes, d) To study the surface wind structures during landfall, e) To investigate the transformation of a cold-core continental mesovortex ...

Abstract The existence of supergradient wind in the interior boundary layer is a distinct feature tropical cyclone (TC). Although vertical advection shown to enhance TC (TCBL), how and what extent strength structure are modulated by not well understood. In this study, both TCBL model an axisymmetric full-physics used quantify contribution process TCBL. Results from show that removal radial redu...

Traditional dictionary learning methods are based on quadratic convex loss function and thus are sensitive to outliers. In this paper, we propose a generic framework for robust dictionary learning based on concave losses. We provide results on composition of concave functions, notably regarding supergradient computations, that are key for developing generic dictionary learning algorithms applic...

We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this paper, we pose it as a combinatorial optimization problem, which is then relaxed to a convex optimization problem that involves searching over the forest and hype...