It is challenging to generate optimal trajectories for nonlinear dynamic systems under external disturbances. In this brief, we present a novel approach planning safe of the chance-constrained trajectory optimization problems with nonconvex constraints. First, chance constraints are handled by deterministic ones which show its availability. We derive an iterative convex method solve control pro...

This paper presents a fuzzy goal programming (FGP) procedure for solving multilevel programming problems (MLPPs) having chance constraints in large hierarchical decision organizations. In the proposed approach, first the chance constraints of a problem are converted into their respective deterministic equivalent in the decision making context. Then, the objective functions of decision makers (D...

As an essential substructure underlying a large class of chance-constrained programming problems with finite discrete distributions, the mixing set with 0 − 1 knapsack has received considerable attentions in recent literature. In this study, we present a family of strong inequalities that subsume known inequalities for this set. We also find many other inequalities that can be explained by lift...

We consider a two player bimatrix game where the entries of the payoff matrices are random variables. We formulate this problem as a chance-constrained game by considering that the payoff of each player is defined using a chance constraint. We consider the case where the entries of the payoff matrices are independent normal/Cauchy random variables. We show a one-to-one correspondence between a ...

We consider fuzzy stochastic programming problems with a crisp objective function and linear constraints whose coefficients are fuzzy random variables, in particular of type L-R. To solve this type of problems, we formulate deterministic counterparts of chance-constrained programming with fuzzy stochastic coefficients, by combining constraints on probability of satisfying constraints, as well a...

We consider chance-constrained programs in which the probability distribution of the random parameters is deterministic and known. Two prominent approaches to deal with these programs are sampling approximations and robust approximations. In the last decade, there has been enormous interest in both these areas of research. This article aims to provide a brief summary of a select number of publi...