Convex underestimators of a polynomial on a box. Given a non convex polynomial <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${f\in \mathbb{R}[{\rm x}]}$$</EquationSource> </InlineEquation> and a box <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${{\rm B}\subset \mathbb{R}^n}$$</EquationSource> </InlineEquation>, we construct a sequence of convex polynomials <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$${(f_{dk})\subset \mathbb{R}[{\rm x}]}$$</EquationSource> </InlineEquation>, which converges in a strong sense to the...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

The paper shows that the global resolution of a general convex quadratic program with complementarity constraints (QPCC), possibly infeasible or unbounded, can be accomplished in finite time. The method constructs a minmax mixed integer formulation by introducing finitely many binary variables,...

In a real situation, optimization problems often involve uncertain parameters. Robust optimization is one of distribution-free methodologies based on worst-case analyses for handling such problems. In this paper, we first focus on a special class of uncertain linear programs (LPs). Applying the...

Extreme events occur rarely, but these are often the circumstances where an insurance coverage is demanded. Given the first, say, n moments of the risk(s) of the events, one is able to compute or approximate the tight bounds for risk measures in the form of E(ψ(x)) through semidefinite...