We consider an optimization problem of minimization of a linear function subject to the chance constraint Prob{G(x, ξ) ∈ C} ≥ 1 − ε, where C is a convex set, G(x, ξ) is bi-affine mapping and ξ is a vector of random perturbations with known distribution. When C is multi-dimensional and ε is small, like 10−6 or 10−10, this problem is, generically, a problem of minimizing under a nonconvex and dif...

Many engineering problems can be cast as optimization problems subject to convex constraints that are parameterized by an uncertainty or 'instance' parameter. Two main approaches are generally available to tackle constrained optimization problems in presence of uncertainty: robust optimization and chance-constrained optimization. Robust optimization is a deterministic paradigm where one seeks a...

Existing electricity market designs assume risk neutrality and lack risk-hedging instruments, which leads to suboptimal outcomes reduces the overall efficiency. This letter enables risk-trading in chance-constrained stochastic by introducing Arrow-Debreu Securities (ADS) derives a risk-averse market-clearing model with trading. To enable trading, probability space of underlying uncertainty is d...

This paper proposes a new optimization techniques for the optimization a gas processing plant uncertain feed and product flows. The problem is first formulated using a continuous linear deterministic approach. Subsequently, the single and joint chance constraint models for steady state process with timedependent uncertainties have been developed. The solution approach is based on converting the...

Island Microgrids can coordinate local energy resources, provide post-fault reliability improvements for customers, and aggregate power resources to offer services the wider system. A crucial component of an Microgrid is battery storage system, which manage imbalances, alleviate constraints, improve by enabling islanding. planning sizing method required quantify maximize benefits while avoiding...

In this paper, we focus on techniques for incremental constraint-based conngu-ration with discrete and continuous variables. We show how to formalize constraint knowledge using compatibility and activity constraints (Mittal 1990) and how this knowledge is used for reasoning within an intelligent CAD system. Most technical (as opposed to spatial) constraint connguration systems use algorithms fo...

In this paper, we focus on techniques for incremen-tal constraint-based connguration with discrete and continuous variables. We show how to formalize constraint knowledge using compatibility and activity constraints (Mittal 1990) and how this knowledge is used for reasoning within an intelligent CAD system. Most technical as opposed to spatial constraint connguration systems use algorithms for ...

We present a brief survey of some of the key results on the interplay between algebraic and graph-theoretic methods in the study of the complexity of digraph-based constraint satisfaction problems. 1998 ACM Subject Classification A.1 Introductory and Survey, D.3.2 Constraint and Logic Languages, F.2.2 Computations on Discrete Structures

Dynamic game arises as a powerful paradigm for multi-robot planning, which safety constraint satisfaction is crucial. Constrained stochastic games are of particular interest, real-world robots need to operate and satisfy constraints under uncertainty. Existing methods solving handle chance using exponential penalties with hand-tuned weights. However, finding suitable penalty weight nontrivial r...