AMS classification: 90C22, 20Cxx, 70-08

We consider the computational complexity of optimizing various classes of continuous functions over a simplex, hypercube or sphere.These relatively simple optimization problems have many applications.We review known approximation results as well as negative (inapproximability) results from the...

AMS classifications: 05C69; 90C35; 90C22;

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...

Portfolio optimization problems involving value at risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains...

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...

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>