More than three decades ago, Boyd and Balakrishnan established a regularity result for the two-norm of a transfer function at maximizers. Their result extends easily to the statement that the maximum eigenvalue of a univariate real analytic Hermitian matrix family is twice continuously differentiable, with Lipschitz second derivative, at all local maximizers, a property that … Read more
The s-clubs model cohesive social subgroups as vertex subsets that induce subgraphs of diameter at most s. In defender-attacker settings, for low values of s, they can represent tightly-knit communities whose operation is undesirable for the defender. For instance, in online social networks, large communities of malicious accounts can effectively propagate undesirable rumors. In this … Read more
This work is devoted to studying an Accelerated Stochastic Peaceman-Rachford Splitting Method (AS-PRSM) for solving a family of structural empirical risk minimization problems. The objective function to be optimized is the sum of a possibly nonsmooth convex function and a finite-sum of smooth convex component functions. The smooth subproblem in AS-PRSM is solved by a stochastic gradient method using variance reduction … Read more
We consider mixed-integer optimal control problems, whose optimality conditions involve global combinatorial optimization aspects for the corresponding Hamiltonian pointwise in time. We propose a time-domain decomposition, which makes this problem class accessible for mixed-integer programming using parallel-in-time direct discretizations. The approach is based on a decomposition of the optimality system and the interpretation of the … Read more
Autonomous vertical farms (VFs) are becoming increasingly more popular, because they allow to grow food minimising water consumption and the use of pesticides, while greatly increasing the yield per square metre, compared with traditional agriculture. To meet sustainability goals, however, VFs must operate at maximum efficiency; it would be otherwise impossible to compete with the … Read more
Cut-generating linear programs (CGLPs) play a key role as a separation oracle to produce valid inequalities for the feasible region of mixed-integer programs. When incorporated inside branch-and-bound, the cutting planes obtained from CGLPs help to tighten relaxations and improve dual bounds. However, running the CGLPs at the nodes of the branch-and-bound tree is computationally cumbersome … Read more
General quadratic optimization problems with linear constraints and additional indicator constraints on the variables are studied. Based on the well-known perspective reformulation for mixed-integer quadratic optimization problems, projective cuts are introduced as new valid inequalities for the general problem. The key idea behind the theory of these cutting planes is the projection of the continuous … Read more
In this paper we study a class of derivative-free nonmonotone line search methods for solving nonlinear systems of equations, which includes the method N-DF-SANE proposed in (IMA J. Numer. Anal. 29: 814–825, 2009). These methods correspond to derivative-free optimization methods applied to the minimization of a suitable merit function. Assuming that the mapping defining the … Read more
We study the exact convergence rate of the alternating projection method for the nontransversal intersection of a semialgebraic set and a linear subspace. If the linear subspace is a line, the exact rates are expressed by multiplicities of the defining polynomials of the semialgebraic set, or related power series. Our methods are also applied to … Read more
In machine learning (ML) applications, unfair predictions may discriminate against a minority group. Most existing approaches for fair machine learning (FML) treat fairness as a constraint or a penalization term in the optimization of a ML model, which does not lead to the discovery of the complete landscape of the trade-offs among learning accuracy and … Read more