We show that a strong upper bound on the objective of the alternating current optimal power flow (ACOPF) problem can significantly improve the effectiveness of optimization-based bounds tightening (OBBT) on a number of relaxations. We additionally compare the performance of relaxations of the ACOPF problem, including the rectangular form without reference bus constraints, the rectangular … Read more
One of the relevant research topics to which Chris Floudas contributed was quadratically constrained quadratic programming (QCQP). This paper considers one of the simplest hard cases of QCQP, the two trust region subproblem (TTRS). In this case, one needs to minimize a quadratic function constrained by the intersection of two ellipsoids. The Lagrangian dual of … Read more
A bipartite bilinear program (BBP) is a quadratically constrained quadratic optimization problem where the variables can be partitioned into two sets such that fixing the variables in any one of the sets results in a linear program. We propose a new second order cone representable (SOCP) relaxation for BBP, which we show is stronger than … Read more
Discretization-based algorithms are proposed for the global solution of mixed-integer nonlinear generalized semi-infinite (GSIP) and bilevel (BLP) programs with lower-level equality constraints coupling the lower and upper level. The algorithms are extensions, respectively, of the algorithm proposed by Mitsos and Tsoukalas (J Glob Optim 61(1):1–17, 2015. https://doi.org/10.1007/s10898-014-0146-6) and by Mitsos (J Glob Optim 47(4):557–582, 2010. … Read more
This paper studies the problem of multi-plant manganese alloy production. The problem consists of finding the optimal furnace feed of ores, fluxes, coke, and slag that yields output products which meet customer specifications, and to optimally decide the volume, composition, and allocation of the slag. To solve the problem, a nonlinear pooling problem formulation is … Read more
Tight convex and concave relaxations are of high importance in the field of deterministic global optimization. We present a heuristic to tighten relaxations obtained by the McCormick technique. We use the McCormick subgradient propagation (Mitsos et al., SIAM J. Optim., 2009) to construct simple affine under- and overestimators of each factor of the original factorable … Read more
We describe BASBL, our implementation of the deterministic global optimization algorithm Branch-and-Sandwich for nonconvex/nonlinear bilevel problems, within the open-source MINOTAUR framework. The solver incorporates the original Branch-and-Sandwich algorithm and modifications proposed in the first part of this work. We also introduce BASBLib, an extensive online library of bilevel benchmark problems collected from the literature and … Read more
In this paper, we consider a fundamental problem in modern digital communications known as multi-input multi-output (MIMO) detection, which can be formulated as a complex quadratic programming problem subject to unit-modulus and discrete argument constraints. Various semidefinite relaxation (SDR) based algorithms have been proposed to solve the problem in the literature. In this paper, we … Read more
We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem. Our approach combines both speed and heading control and provides global optimality guarantees despite non-convexities in the feasible region. As a side result, we present a new characterization of the conflict separation condition in the form of … Read more
Alternating current optimal power flow (AC OPF) is one of the most fundamental optimization problems in electrical power systems. It can be formulated as a semidefinite program (SDP) with rank constraints. Solving AC OPF, that is, obtaining near optimal primal solutions as well as high quality dual bounds for this non-convex program, presents a major … Read more