A regular timetable is a collection of events that repeat themselves every specific time span. This even structure, whenever applied at a whole network, leads to several benefits both for users and the company, although some issues are introduced, especially about dimensioning the service. It is therefore fundamental to properly consider the interaction between the … Read more
In this paper we present a four-level market model that accounts for airport capacity extension, fleet investment, aircraft scheduling, and ticket trade in a liberalized aviation market with independent decision makers. In particular, budget-constrained airports decide on the first level on their optimal runway capacity extension and on a corresponding airport charge. Airports anticipate optimal … Read more
This study looks at the application of mathematical concepts of entropy and Fibonacci sequence in creating optimal dimensional relations of classification character. The paper is devoted to optimization of some numerical relations and integers as unified threshold characteristics of classification type, aimed for example at systemic optimizing the measuring information of various processes. The paper … Read more
We focus on solving robust principal component analysis (RPCA) arising from various applications such as information theory, statistics, engineering, and etc. We adopt a model to minimize the sum of observation error and sparsity measurement subject to the rank constraint. To solve this problem, we propose a two-step alternating minimization method. In one step, a … Read more
In this paper, we propose a partial convolution model for image delburring and denoising. We also devise a new linearized alternating direction method of multipliers (ADMM) with extension step. On one hand, the computation of its subproblem is dominated by several FFTs, hence its per-iteration cost is low, on the other hand, the relaxed parameter … Read more
\ys{This paper introduces} a symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming \ys{with linear equality constraints, which inherits the superiorities of the classical alternating direction method of multipliers (ADMM), and extends the feasible set of the relaxation factor $\alpha$ of the generalized ADMM to the infinite interval $[1,+\infty)$}. … Read more
In this paper we consider interchangeability of the minimization operator with monotone risk functionals. In particular we discuss the role of strict monotonicity of the risk functionals. We also discuss implications to solutions of dynamic programming equations of risk averse multistage stochastic programming problems. ArticleDownload View PDF
We consider solving unconstrained optimization problems by means of two popular globalization techniques: trust-region (TR) algorithms and adaptive regularized framework using cubics (ARC). Both techniques require the solution of a so-called “subproblem” in which a trial step is computed by solving an optimization problem involving an approximation of the objective function, called “the model”. The … Read more
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
Cutting planes are derived from specific problem structures, such as a single linear constraint from an integer program. This paper introduces cuts that involve minimal structural assumptions, enabling the generation of strong polyhedral relaxations for a broad class of problems. We consider valid inequalities for the set $S\cap P$, where $S$ is a closed set, … Read more