State-of-charge (SoC) dependent bidding allows merchant storage participants to incorporate SoC-dependent operation and opportunity costs in a bid-based market clearing process. However, such bid results non-convex cost function the multi-interval economic dispatch clearing, limiting its implementation practice. We show that simple restriction on format removes non-convexity, making of bids sta...

The phrase convex optimization refers to the minimization of a convex function over a convex set. However the feasible convex set need not be always described by convex inequalities. In this article we consider a convex feasible set which are described by inequality constraints which are locally Lipschitz and not necessarily convex and need not be smooth. We show that if the Slater’s constraint...

This paper introduces a fundamental family of unbounded convex sets that arises in the context of non-convex mixed-integer quadratic programming. It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a set in the family. Some fundamental properties of the convex sets are derived, along with connections to some o...

The paper develops a dynamic economic model of a controlled biological invasion. Such problems are inherently non-convex for two reasons. First, the invasion growth function and the set of feasible time paths may be non-convex. Second, non-convexities in the objective function may arise naturally from the fact that control costs depend on the invasion size. The goal of this paper is to characte...

let $c_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{d}$. each function $f in c_{0}(alpha)$ maps the unit disk $mathbb{d}$ onto the complement of an unbounded convex set. in this paper, we study the mapping properties of this class under integral operators.