When using interior point methods for solving semidefinite programs (SDP), one needs to solve a system of linear equations at each iteration. For problems of large size, solving the system of linear equations can be very expensive. In this paper, we propose a trust region algorithm for solving...

The stable-set problem is an NP-hard problem that arises in numerous areas such as social networking, electrical engineering, environmental forest planning, bioinformatics clustering and prediction, and computational chemistry. While some relaxations provide high-quality bounds, they result in...

The stable-set problem is an NP-hard problem that arises in numerous areas such as social networking, electrical engineering, environmental forest planning, bioinformatics clustering and prediction, and computational chemistry. While some relaxations provide high-quality bounds, they result in...

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...

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,...