We define the inclusion certificate as a measure that expresses each point in the domain of a collection of functions as a convex combination of other points in the domain. Using inclusion certificates, we extend the convex extensions theory to enable simultaneous convexification of functions. We discuss conditions under which the domain of the functions can be reduced without affecting the sim...

This paper is concerned with the minimum-cost flow problem over an arbitrary flow network. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non...

The goal of this paper is threefold. It first describes a novel way of measuring disagreement between rankings of a finite set X of n ≥ 1 elements, that can be viewed as a (mass transportation) Kantorovich metric, once the collection rankings of X is embedded in the set Kn of n× n doubly-stochastic matrices. It also shows that such an embedding makes it possible to define a natural notion of me...

This work investigates the computational procedures used to obtain global solution to the Economic Linear Optimal Control (ELOC) problem. The proposed method employs the Generalized Benders Decomposition (GBD) algorithm. Compared to the previous branch and bound approach, a naive application GBD to the ELOC problem will improve computational performance, due to less frequent calls to computatio...

We consider in this paper the homogeneous 1-D wave equation defined on Ω ⊂ R. Using the Hilbert Uniqueness Method, one may define, for each subset ω ⊂ Ω, the exact control vω of minimal L (ω × (0, T ))-norm which drives to rest the system at a large enough time T > 0. We address the question of the optimal position of ω which minimizes the functional J : ω → ||vω||L2(ω×(0,T )). We express the s...

We propose the moment cone relaxation for a class of polynomial optimization problems (POPs) to extend the results on the completely positive cone programming relaxation for the quadratic optimization (QOP) model by Arima, Kim and Kojima. The moment cone relaxation is constructed to take advantage of sparsity of the POPs, so that efficient numerical methods can be developed in the future. We es...

Rapid and accurate rendezvous proximity operations for spacecraft are crucial to the success of most space missions. In this paper, a sequential convex programming method, combined with first-order second-order Birkhoff pseudospectral methods, is proposed autonomous spacecraft. The original nonlinear nonconvex close-range problem thrust constraints no-fly zone converted into its version by usin...