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WGSCO 2018, Workshop on Graph Spectra, Combinatorics and Optimizationwas successfully held in the University of Aveiro, Portugal, at the occasion of the 65th birthday of Professor Domingos M. Cardoso. The topics of the Workshop reflected the diversity of the scientific interests of Prof. DomingosM. Cardoso and themain lines of research of the Group onGraph Theory, Optimization and Combinatorics, which had been coordinated by him duringmany years within the ResearchUnit CIDMAof theMathematics Department of the University of Aveiro: Algebraic Combinatorics, Algebraic Graph Theory, Algorithms and Computing Techniques, Combinatorial Optimization, Communications and Control Theory, Enumerative and Extremal Combinatorics, Graph Theory, Optimization in Graphs, Graph Spectra and Applications, Linear Optimization, Networks, Nonlinear Optimization, and others. TheWorkshop counted with 8 invited plenary talks, 80 contributed talks, and was assisted by more than 100 participants from 27 countries. For this special issue, participants of the WGSCO2018 were invited to submit papers on optimization, control and related topics. The papers included recent theoretical and applied contributions in various fields of optimization. Based on rigorous reviewing processes, 9 papers were accepted for publication and included in this special issue. Their short descriptions follow subsequently. In his paper entitled ‘A survey on graphs with convex quadratic stability number’, D. Cardoso considers the main challenges in study of graphs with convex quadratic stability number, i.e. the graph for which the stability number is determined by solving a convex quadratic programme. The survey starts with an exposition of some extensions of the classical Motzkin–Straus approach to the determination of the stability number of a graph and its relations with the convex quadratic programming upper bound. The main advances, including several properties and alternative characterizations of graphs with convex quadratic stability number are described as well as the algorithmic strategies developed for their recognition.Openproblems and a conjecture for a particular class of graphs, so-called adverse graphs, are presented, pointing out a research line which is a challenge between continuous and discrete problems. In the paper ‘A parameter method for linear algebra and optimization with uncertainties’,N.Van and I. Van denBerg study systems of linear equations with uncertainties in the coefficients, often representing imprecise data. Formodelling