The following conjecture of Fejes T6th is proved: The density of a lattice of convex bodies in [w” is at least i, provided that each connected component of the complementary set is bounded. The cases of equality are also determined. For any polytope P in [w” one can define a convexification P* (see Section 1) and it is proved that Vol P S Vol P*. It is also shown that if P and P’ are two convex...

We consider the DC optimization problem (P) inf x∈X {(f1(x) − f2(x)) + (g1(Ax) − g2(Ax))}, where f1, f2, g1 and g2 are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y respectively, and A is a linear continuous operator from X to Y . Adopting the standard convexification technique, a Fenchel dual problem of (P) is given. By using properties of the ep...

Optimal control problems are common in aerospace engineering. A Python software program called PySCP is described for solving multiple-phase optimal using sequential convex programming methods. By constructing a series of approximated second-order cone subproblems, approaches to the solution original problem an iterative way. The key components detail, including convexification, discretization,...

For a class of infinite-dimensional minimization problems with nonlinear equality constraints, an iterative algorithm for finding global solutions is suggested. A key assumption is the convexity of the “epigraph”, a set in the product of the image spaces of the constraint and objective functions. A convexification method involving randomization is used. The algorithm is based on the extremal sh...

In the 1990s, in many countries, wages became a more convex function of education: returns to college increased and returns to intermediate education declined. This paper argues that an important cause of this convexification was a two-stage demand-supply interaction: an increased demand for educated workers stimulated a supply response; an increased supply of intermediate-educated workers furt...

This paper is concerned with the power system state estimation (PSSE) problem that aims to find the unknown operating point of a power network based on a given set of measurements. We first study the power flow (PF) problem as an important special case of PSSE, which is known to be non-convex and NP-hard in the worst case. To this end, we propose a set of semidefinite programs (SDPs) with the p...