Joint dynamic probabilistic constraints with projected linear decision rules

We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We establish the relation between the original (infinite dimensional) problem and approximating problems working with projections from different subclasses of decision policies. Considering the subclass of linear decision rules and a generalized linear model for the underlying stochastic process with noises that are Gaussian or truncated Gaussian, we show that the value and gradient of the objective and constraint functions of the approximating problems can be computed analytically

Structural properties of linear probabilistic constraints

The paper provides a structural analysis of the feasible set defined by linear probabilistic constraints. Emphasis is laid on single (individual) probabilistic constraints. A classical convexity result by Van de Panne/Popp and Kataoka is extended to a broader class of distributions and to more general functions of the decision vector. The range of probability levels for which convexity can be expected is exactly identified. Apart from convexity, also nontriviality and compactness of thefeasible set are precisely characterized at the same time. The relation between feasible sets with negative and nonnegative right-hand side is revealed. Finally, an existence result is formulated for the more difficult case of joint probabilistic constraints

Metric regularity and quantitative stability in stochastic programs with probabilistic constraints

Necessary and sufficient conditions for metric regularity of (several joint) probabilistic constraints are derived using recent results from nonsmooth analysis. The conditions apply to fairly general nonconvex, nonsmooth probabilistic constraints and extend earlier work in this direction. Further, a verifiable sufficient condition for quadratic growth of the objective function in a more specific convex stochastic program is indicated and applied in order to obtain a new result on quantitative stability of solution sets when the underlying probability distribution is subjected to perturbations. This is used to establish a large deviation estimate for solution sets when the probability measure is replaced by empirical ones

Measuring of second–order stochastic dominance portfolio efficiency

summary:In this paper, we deal with second-order stochastic dominance (SSD) portfolio efficiency with respect to all portfolios that can be created from a considered set of assets. Assuming scenario approach for distribution of returns several SSD portfolio efficiency tests were proposed. We introduce a $\delta$-SSD portfolio efficiency approach and we analyze the stability of SSD portfolio efficiency and $\delta$-SSD portfolio efficiency classification with respect to changes in scenarios of returns. We propose new SSD and $\delta$-SSD portfolio efficiency measures as measures of the stability. We derive a non-linear and mixed-integer non-linear programs for evaluating these measures. Contrary to all existing SSD portfolio inefficiency measures, these new measures allow us to compare any two $\delta$-SSD efficient or SSD efficient portfolios. Finally, using historical US stock market data, we compute $\delta$-SSD and SSD portfolio efficiency measures of several SSD efficient portfolios

Second-order analysis of polyhedral systems in finite and infinite dimensions with applications to robust stability of variational inequalities

Abstract. This paper concerns second-order analysis for a remarkable class of variational systems in finite-dimensional and infinite-dimensional spaces, which is particularly important for the study of optimization and equilibrium problems with equilibrium constraints. Systems of this type are described via variational inequalities over polyhedral convex sets and allow us to provide a comprehensive local analysis by using appropriate generalized differentiation of the normal cone mappings for such sets. In this paper we efficiently compute the required coderivatives of the normal cone mappings exclusively via the initial data of polyhedral sets in reflexive Banach spaces. This provides the main tools of second-order variational analysis allowing us, in particular, to deriv

Sufficient Conditions for Error Bounds and Applications

Our aim in this paper is to present sufficient conditions for error bounds in terms of Fréchet and limiting Fréchet subdifferentials in general Banach spaces. This allows us to develop sufficient conditions in terms of the approximate subdifferential for systems of the form (x, y) ∈ C × D, g(x, y, u) = 0, where g takes values in an infinite-dimensional space and u plays the role of a parameter. This symmetric structure offers us the choice of imposing conditions either on C or D. We use these results to prove the nonemptiness and weak-star compactness of Fritz–John and Karush–Kuhn–Tucker multiplier sets, to establish the Lipschitz continuity of the value function and to compute its subdifferential and finally to obtain results on local controllability in control problems of nonconvex unbounded differential inclusions

The KCNQ1 channel - remarkable flexibility in gating allows for functional versatility

The KCNQ1 channel (also called Kv7.1 or KvLQT1) belongs to the superfamily of voltage-gated K(+) (Kv) channels. KCNQ1 shares several general features with other Kv channels but also displays a fascinating flexibility in terms of the mechanism of channel gating, which allows KCNQ1 to play different physiological roles in different tissues. This flexibility allows KCNQ1 channels to function as voltage-independent channels in epithelial tissues, whereas KCNQ1 function as voltage-activated channels with very slow kinetics in cardiac tissues. This flexibility is in part provided by the association of KCNQ1 with different accessory KCNE β-subunits and different modulators, but also seems like an integral part of KCNQ1 itself. The aim of this review is to describe the main mechanisms underlying KCNQ1 flexibility