A universal and structured way to derive dual optimization problem formulations

The dual problem of a convex optimization problem can be obtained in a relatively simple and structural way by using a well-known result in convex analysis, namely Fenchel’s duality theorem. This alternative way of forming a strong dual problem is the subject in this paper. We recall some standard results from convex analysis and then … Read more

Computationally tractable counterparts of distributionally robust constraints on risk measures

In optimization problems appearing in fields such as economics, finance, or engineering, it is often important that a risk measure of a decision-dependent random variable stays below a prescribed level. At the same time, the underlying probability distribution determining the risk measure‚Äôs value is typically known only up to a certain degree and the constraint … Read more

Deriving robust counterparts of nonlinear uncertain inequalities

In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It … Read more