This paper deals with several combinatorial optimization problems. The most challenging such problem is the quadratic assignment problem. It is considered in both two dimensions (QAP) and in three dimensions (Q3AP) and in the context of communication engineering. Semidefinite relaxations are used to derive lower bounds for the optimum while heuristics are applied to either … Read more
We shed light on the structure of the “three-operator” version of the forward-Douglas–Rachford splitting algorithm for finding a zero of a sum of maximally monotone operators $A + B + C$, where $B$ is cocoercive, involving only the computation of $B$ and of the resolvent of $A$ and of $C$, separately. We show that it … Read more
We introduce a new constraint system for sparse variable selection in statistical learning. Such a system arises when there are logical conditions on the sparsity of certain unknown model parameters that need to be incorporated into their selection process. Formally, extending a cardinality constraint, an affine sparsity constraint (ASC) is defined by a linear inequality … Read more
We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations … Read more
The main task of genetic regulatory networks is to construct a sparse probabilistic Boolean network (PBN) based on a given transition-probability matrix and a set of Boolean networks (BNs). In this paper, a Bregman alternating direction method of multipliers (BADMM) is proposed to solve the minimization problem raised in PBN. All the customized subproblem-solvers of … Read more
We study distributionally robust optimization (DRO) problems where the ambiguity set is de ned using the Wasserstein metric. We show that this class of DRO problems can be reformulated as semi-in nite programs. We give an exchange method to solve the reformulated problem for the general nonlinear model, and a central cutting-surface method for the convex case, … Read more
Range anxiety, the persistent worry about not having enough battery power to complete a trip, remains one of the major obstacles to widespread electric-vehicle adoption. As cities look to attract more users to adopt electric vehicles, the emergence of wireless in-motion car charging technology presents itself as a solution to range anxiety. For a limited … Read more
Automatic Differentiation (AD) is applied to the open-source CAD system Open CASCADE Technology using the AD software tool ADOL-C (Automatic Differentiation by OverLoading in C++). The differentiated CAD system is coupled with a discrete adjoint CFD solver, thus providing the first example of a complete differentiated design chain built from generic, multi-purpose tools. The design … Read more
Motivated by its implications in the development of general purpose solvers for decomposable Mixed Integer Programs (MIP), we address a fundamental research question, that is to assess if good decomposition patterns can be consistently found by looking only at static properties of MIP input instances, or not. We adopt a data driven approach, devising a … Read more
We develop polynomial-time heuristic methods to solve unimodular quadratic programs (UQPs) approximately, which are known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit modulus. Several problems in active sensing and wireless communication applications boil down to UQP. With this motivation, we present three … Read more