Sequential quadratic programming (SQP) methods solve nonlinear optimization problems by finding an approximate solution of a sequence of quadratic programming (QP) subproblems. Each subproblem involves the minimization of a quadratic model of the objective function subject to the linearized constraints. Depending on the definition of the quadratic model, the QP subproblem may be nonconvex, lead...

Abstract. We study some properties of the randomized series and their applications to the geometric structure of Banach spaces. For n ≥ 2 and 1 < p < ∞, it is shown that l ∞ is representable in a Banach space X if and only if it is representable in the Lebesgue-Bochner Lp(X). New criteria for various convexity properties in Banach spaces are also studied. It is proved that a Banach lattice E is...

A convexification method is proposed for solving a class of global optimization problems with certain monotone properties. It is shown that this class of problems can be transformed into equivalent concave minimization problems using the proposed convexification schemes. An outer approximation method can then be used to find the global solution of the transformed problem. Applications to mixed-...

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...

Unstructured tetrahedral grids are a common data representation of three-dimensional scalar fields. For convex unstructured meshes efficient rendering methods are known. For concave or cyclic meshes, however, a significant overhead is required to sort the grid cells in back to front order. In this paper we apply methods known from computational geometry to transform concave into convex grids. W...

We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we ...

Abstract—We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial netw...

We address here a class of particularly hard-to-solve combinatorial optimization problems namely multicommodity network optimization when the link cost functions are discontinuous step increasing. The main focus is on the development of relaxations for such problems in order to derive lower bounds. A straightforward way of getting lower bounds is to solve the “convexification” of the problem, i...