It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load over-satisfaction. In this paper, we investigate the situation where generation lower bounds are present. We show that even for a … Read more
Covering problems are well studied in the Operations Research literature under the assumption that both the set of users and the set of potential facilities are finite. In this paper we address the following variant, which leads to a Mixed Integer Nonlinear Program (MINLP): locations of p facilities are sought along the edges of a … Read more
This paper presents a method for finding global optima to constrained nonlinear programs via slack variables. The method only applies if all functions involved are of class C1 but without any further qualification on the types of constraints allowed; it proceeds by reformulating the given program into a bi-objective program that is then solved for … Read more
We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch-and-bound algorithm for convex quadratic mixed integer programming problems. The branch-and-bound algorithm generalizes the approach for unconstrained convex quadratic integer programming proposed by Buchheim, Caprara and Lodi to the presence … Read more
We study the minimization of fixed-degree polynomials over the simplex. This problem is well-known to be NP-hard, as it contains the maximum stable set problem in graph theory as a special case. In this paper, we consider a rational approximation by taking the minimum over the regular grid, which consists of rational points with denominator … Read more
This paper presents a relatively “unfettered” method for finding global optima to constrained nonlinear programs. The method reformulates the given program into a bi-objective mixed-integer program that is then solved for the Nash equilibrium. A numerical example (whose solution provides a new benchmark against which other algorithms may be assessed) is included to illustrate the … Read more
In rigorous constrained global optimization, upper bounds on the objective function help to reduce the search space. Their construction requires finding a narrow box around an approximately feasible solution, verified to contain a feasible point. Approximations are easily found by local optimization, but the verification often fails. In this paper we show that even if … Read more
This work deals with a Huff-like Stackelberg problem, where the leader facility wants to decide its location so that its profit is maximal after the competitor (the follower) also built its facility. It is assumed that the follower makes a rational decision, maximizing their profit. The inelastic demand is aggregated into the vertices of a … Read more
We propose a new method for solving univariate global optimization problems by combining a lower bound function of ®BB method (see [1]) with the lower bound function of the method developed in [4]. The new lower bound function is better than the two lower bound functions. We add the convex/concave test and pruning step which … Read more
In this article we survey mathematical programming approaches to problems in the field of water network optimization. Predominant in the literature are two different, but related problem classes. One can be described by the notion of network design, while the other is more aptly termed by network operation. The basic underlying model in both cases … Read more