Using results from parametric optimization, we derive for chance-constrained stochastic programs quantitative stability properties for locally optimal values and sets of local minimizers when the underlying probability distribution is subjected to perturbations in a metric space of probability measures. Emphasis is placed on verifiable sufficient conditions for the constraint-set mapping to ful...

In this paper we develop convex relaxations of chance constrained optimization problems in order to obtain lower bounds on the optimal value. Unlike existing statistical lower bounding techniques, our approach is designed to provide deterministic lower bounds. We show that a version of the proposed scheme leads to a tractable convex relaxation when the chance constraint function is affine with ...

We study joint chance constrained programs (JCCPs). JCCPs are often non-convex and non-smooth, and thus are generally challenging to solve. In this paper, we propose a logarithmsum-exponential smoothing technique to approximate a joint chance constraint by the difference of two smooth convex functions and use a sequential convex approximation algorithm, coupled with a Monte Carlo method, to sol...

Despite the importance of pointing-device movement to efficiency in interfaces, little is known on how target shape impacts speed, acceleration, and other kinematic properties of motion. In this paper, we examine which kinematic characteristics of motion are impacted by amplitude and directional target constraints in Fitts-style pointing tasks. Our results show that instantaneous speed, acceler...

In this work we introduce a novel approach, based on sampling, for finding policies that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the original problem being analysed and it guarantees that, with a given confidence probability, the policies produced by solving this reduced problem satisfy the ...

The wide applicability of chance–constrained programming, together with advances in convex optimization and probability theory, has created a surge of interest in finding efficient methods for processing chance constraints in recent years. One of the successes is the development of so–called safe tractable approximations of chance–constrained programs, where a chance constraint is replaced by a...

Motivated by a class of chance-constrained optimization problems, we explore modifications of the (generalized) Benders’ decomposition approach. The chance-constrained problems we consider involve a random variable with an underlying discrete distribution, are convex in the decision variable, but their probabilistic constraint is neither separable nor linear. The variants of Benders’ approach w...

In this paper we study ambiguous chance constrained problems where the distributions of the random parameters in the problem are themselves uncertain. We primarily focus on the special case where the uncertainty set Q of the distributions is of the form Q = {Q : ρp(Q, Q0) ≤ β}, where ρp denotes the Prohorov metric. The ambiguous chance constrained problem is approximated by a robust sampled pro...

We consider a chance constrained problem, where one seeks to minimize a convex objective over solutions satisfying, with a given close to one probability, a system of randomly perturbed convex constraints. Our goal is to build a computationally tractable approximation of this (typically intractable) problem, i.e., an explicitly given deterministic optimization program with the feasible set cont...