The aim of this paper is to propose a solution algorithm for a particular class of rank-two nonconvex programs having a polyhedral feasible region. The algorithm lies within the class of the so called “optimal level solutions” parametric methods. The subproblems obtained by means of this...

In this paper we consider a class of generalized quasi-variational inequalities. The variational problem is studied in the convex set <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$X\times Y$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>X</mi> <mo>×</mo> <mi>Y</mi> </mrow> </math> </EquationSource> </InlineEquation>, with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$Y$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>Y</mi> </math> </EquationSource> </InlineEquation> bounded and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$X$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>X</mi> </math> </EquationSource> </InlineEquation> unbounded. In the latter settings, we investigate about the solvability of the problem....</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

The coloring of disk graphs is motivated by the frequency assignment problem. In 1998, Malesińska et al. introduced double disk graphs as their generalization. They showed that the chromatic number of a double disk graph <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$G$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>G</mi> </math> </EquationSource> </InlineEquation> is at most <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$33\,\omega (G) - 35$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>33</mn> <mspace width="0.166667em"/> <mi mathvariant="italic">ω</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> <mo>-</mo> <mn>35</mn> </mrow> </math> </EquationSource>...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

Two approximation algorithms for solving convex vector optimization problems (CVOPs) are provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously. The first algorithm is an extension of Benson’s outer approximation algorithm, and the second one is a dual variant...

In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization...

Solving transportation problems is essential in engineering and supply chain management, where profitability depends on optimal traffic flow. This study proposes risk-control approaches for two bottleneck transportation problems with random variables and preference levels to objective functions...

The biggest challenge when disclosing private data is to share information contained in databases while protecting people from being individually identified. Microaggregation is a family of methods for statistical disclosure control. The principle of microaggregation is that confidentiality...

The paper provides the construction of error-correcting pooling designs with the incidence matrix of two types of subspaces of symplectic spaces over finite fields. As a generalization of Guo et al.’s matrix, we use the general subspaces of type <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(m,s)$$</EquationSource> </InlineEquation> to substitute special subspaces of...</equationsource></inlineequation>

This manuscript introduces ANTIGONE, Algorithms for coNTinuous/Integer Global Optimization of Nonlinear Equations, a general mixed-integer nonlinear global optimization framework. ANTIGONE is the evolution of the Global Mixed-Integer Quadratic Optimizer, GloMIQO, to general nonconvex terms. The...

We propose variants of non-asymptotic dual transcriptions for the functional inequality of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$ f + g + k\circ H \ge h$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>f</mi> <mo>+</mo> <mi>g</mi> <mo>+</mo> <mi>k</mi> <mo>∘</mo> <mi>H</mi> <mo>≥</mo> <mi>h</mi> </mrow> </math> </EquationSource> </InlineEquation>. The main tool we used consists in purely algebraic formulas on the epigraph of the Legendre-Fenchel transform of the function <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$ f + g +...</equationsource></inlineequation></equationsource></equationsource></inlineequation>