This paper introduces a novel approach to integrals with respect to capacities. Any random variable is decomposed as a combination of indicators. A prespecified set of collections of events indicates which decompositions are allowed and which are not. Each allowable decomposition has a value determined by the capacity. The decomposition-integral of a random variable is defined as the highest of...

This paper introduces a novel approach to integrals with respect to capacities. Any random variable is decomposed as a combination of indicators. A pre-speci ed set of collections of events indicates which decompositions are allowed and which are not. Each allowable decomposition has a value determined by the capacity. The decomposition-integral of a random variable is de ned as the highest of ...

This paper presents a new class of intelligent systems, called Evolutionary Ruin and Stochastic Recreate, that can learn and adapt to the changing enviroment. It improves the original Ruin and Recreate principle’s performance by incorporating an Evolutionary Ruin step which implements evolution within a single solution. In the proposed approach, a cycle of Solution Decomposition, Evolutionary R...

The central theme of this paper is multiplicative polynomial dimensional decomposition (PDD) methods for solving high-dimensional stochastic problems. When a stochastic response is dominantly of multiplicative nature, the standard PDD approximation, predicated on additive function decomposition, may not provide sufficiently accurate probabilistic solutions of a complex system. To circumvent thi...

We analyze stochastic gradient descent for optimizing non-convex functions. In many cases for non-convex functions the goal is to find a reasonable local minimum, and the main concern is that gradient updates are trapped in saddle points. In this paper we identify strict saddle property for non-convex problem that allows for efficient optimization. Using this property we show that from an arbit...

A power generation system comprising thermal and pumped storage hy dro plants is considered Two kinds of models for the cost optimal generation of electric power under uncertain load are introduced i a dynamic model for the short term operation and ii a power production planning model In both cases the presence of stochastic data in the optimization model leads to multi stage and two stage stoc...

Traditional two-stage stochastic programming is risk-neutral; that is, it considers the expectation as the preference criterion while comparing the random variables (e.g., total cost) to identify the best decisions. However, in the presence of variability risk measures should be incorporated into decision making problems in order to model its effects. In this study, we consider a risk-averse tw...

Jangwoon Lee* ([email protected]), University of Mary Washington, Department of Mathematics, 1301 College Ave, Fredericksburg, VA 22401, and Jeehyun Lee and Yoongu Hwang. An Optimization Based Domain Decomposition Method for PDEs with Random Inputs. An optimization-based domain decomposition method for stochastic elliptic partial differential equations is presented. The main idea of the method is a...