A copositive approach for two-stage adjustable robust optimization with uncertain right-hand sides
We study two-stage adjustable robust linear programming in which the right-hand sides are
uncertain and belong to a convex, compact uncertainty set. This problem is NP-hard, and the …
uncertain and belong to a convex, compact uncertainty set. This problem is NP-hard, and the …
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 …
computing the stability number of a graph. Our work is based on and refines de Klerk and …
A PTAS for the minimization of polynomials of fixed degree over the simplex
We consider the problem of computing the minimum value pmin taken by a polynomial p (x)
of degree d over the standard simplex Δ. This is an NP-hard problem already for degree d …
of degree d over the standard simplex Δ. This is an NP-hard problem already for degree d …
Completely positive reformulations for polynomial optimization
Polynomial optimization encompasses a very rich class of problems in which both the
objective and constraints can be written in terms of polynomials on the decision variables …
objective and constraints can be written in terms of polynomials on the decision variables …
Representing quadratically constrained quadratic programs as generalized copositive programs
We show that any (nonconvex) quadratically constrained quadratic program (QCQP) can be
represented as a generalized copositive program. In fact, we provide two representations …
represented as a generalized copositive program. In fact, we provide two representations …
Think co (mpletely) positive! Matrix properties, examples and a clustered bibliography on copositive optimization
IM Bomze, W Schachinger, G Uchida - Journal of Global Optimization, 2012 - Springer
Copositive optimization is a quickly expanding scientific research domain with wide-spread
applications ranging from global nonconvex problems in engineering to NP-hard …
applications ranging from global nonconvex problems in engineering to NP-hard …
Strong duality and minimal representations for cone optimization
L Tunçel, H Wolkowicz - Computational optimization and applications, 2012 - Springer
The elegant theoretical results for strong duality and strict complementarity for linear
programming, LP, lie behind the success of current algorithms. In addition, preprocessing is …
programming, LP, lie behind the success of current algorithms. In addition, preprocessing is …
KKT solution and conic relaxation for solving quadratically constrained quadratic programming problems
To find a global optimal solution to the quadratically constrained quadratic programming
problem, we explore the relationship between its Lagrangian multipliers and related linear …
problem, we explore the relationship between its Lagrangian multipliers and related linear …
LP-based Construction of DC Decompositions for Efficient Inference of Markov Random Fields
C Murti, D Kashyap… - … Conference on Artificial …, 2024 - proceedings.mlr.press
The success of the convex-concave procedure (CCCP), a widely used technique for non-
convex optimization, crucially depends on finding a decomposition of the objective function …
convex optimization, crucially depends on finding a decomposition of the objective function …
[HTML][HTML] On the exactness of sum-of-squares approximations for the cone of 5× 5 copositive matrices
We investigate the hierarchy of conic inner approximations K n (r)(r∈ N) for the copositive
cone COP n, introduced by Parrilo (2000)[22]. It is known that COP 4= K 4 (0) and that, while …
cone COP n, introduced by Parrilo (2000)[22]. It is known that COP 4= K 4 (0) and that, while …