In this paper, we study iteration complexities of Mizuno-Todd-Ye predictor-corrector (MTY-PC) algorithms in SDP and symmetric cone programs by way of curvature integrals. The curvature integral is defined along the central path, reflecting the geometric structure of the central path. Integrating...

This paper addresses the general continuous single facility location problems in finite dimension spaces under possibly different <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\ell _\tau $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>ℓ</mi> <mi mathvariant="italic">τ</mi> </msub> </math> </EquationSource> </InlineEquation> norms, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$\tau \ge 1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="italic">τ</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>, in the demand points. We analyze the difficulty of this family of problems and revisit...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

A semi-definite programming (SDP) formulation of the multi-objective economic-emission dispatch problem is presented. The fuel cost and emission functions are represented by high order polynomial functions and this was shown to be a more accurate representation of the economic-emission dispatch...