In the paper we consider the chance-constrained version of an affinely perturbed linear matrix inequality (LMI) constraint, assuming the primitive perturbations to be independent with light-tail distributions (e.g., bounded or Gaussian). Constraints of this type, playing a central role in chance-constrained linear/conic quadratic/semidefinite programming, are typically computationally intractab...

The water environment restoration project portfolio (WERP) selection is discussed in this paper. By complying with the analysis of project’s multidimensional property and operation mode, paper develops chance constraint management WERP from perspectives public service enterprise operation. In addition, multi-objective mixed integer linear programming model constructed by combining expectation m...

In this paper, we deal with a hydraulic reservoir optimization problem with uncertainty on inflows in a joint chance constrained programming setting. In particular, we will consider inflows with a persistency effect, following a causal time series model, and examine the impact of the ”Gaussian” assumption for such inflows. We present an iterative algorithm for solving similarly structured joint...

In this paper, a novel approach for multi response optimization is presented. In the proposed approach, response variables in treatments combination occur with a certain probability. Moreover, we assume that each treatment has a network style. Because of the probabilistic nature of treatment combination, the proposed approach can compute the efficiency of each treatment under the desirable reli...

We propose a method for learning constraints represented as Gaussian processes (GPs) from locally-optimal demonstrations. Our approach uses the Karush-Kuhn-Tucker (KKT) optimality conditions to determine where on demonstrations constraint is tight, and scaling of gradient at those states. then train GP representation which consistent with generalizes this information. further show that uncertai...

We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosen penalty-type objectives. We show that the two problems are asymptotically equivalent. Simpler cases with one chance constraint and particular penalty functions were studied in [6, 11]. The obtained problems with penalties and with a fixed set of feasible so...

The mixing set with a knapsack constraint arises in deterministic equivalent of chance-constrained programming problems with finite discrete distributions. We first consider the case that the chance-constrained program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit ine...

Abstract We consider an n -player non-cooperative game where the payoff function of each player follows a multivariate distribution. This formulation is adopted to model zonal electricity market in which generators operate by running conventional and renewable-based plants. The players compete as Cournot model. formulate this problem chance-constrained defining using chance constraint. A full e...