Luis F. Zuluaga

Computing the Stability Number of a Graph Via Linear and Semidefinite Programming

We study certain linear and semidefinite programming lifting approximation schemes for computing the stability number of a graph. Our work is based on and refines de Klerk and Pasechnik’s approach to approximating the stability number via copositive programming [SIAM J. Optim., 12 (2002), pp. 875-892]. We provide a closed-form expression for the values computed by the linear programming approximations. We also show that the exact value of the stability number

LMI Approximations for Cones of Positive Semidefinite Forms

\alpha(G)

A Conic Programming Approach to Generalized Tchebycheff Inequalities

is attained by the semidefinite approximation of order

Mortality Portfolio Risk Management

\alpha(G)-1

Completely positive reformulations for polynomial optimization

as long as

Static-arbitrage lower bounds on the prices of basket options via linear programming

\alpha(G) \leq 6

Technical Note---A Risk- and Ambiguity-Averse Extension of the Max-Min Newsvendor Order Formula

. Our results reveal some sharp differences between the linear and the semidefinite approximations. For instance, the value of the linear programming approximation of any order is strictly larger than

Optimizing Highway Transportation at the United States Postal Service

\alpha(G)

Third-order extensions of Lo's semiparametric bound for European call options

whenever

Alternative LP and SOCP Hierarchies for ACOPF Problems

\alpha(G) > 1