Convergent Semidefinite Programming Relaxations for Global Bilevel Polynomial Optimization Problems
نویسندگان
چکیده
منابع مشابه
Convergent Semidefinite Programming Relaxations for Global Bilevel Polynomial Optimization Problems
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and global minimum using a sequence of semidefinite programming (SDP) relaxations and provide convergence results for the methods. Our scheme for problems with a ...
متن کاملEquality Based Contraction of Semidefinite Programming Relaxations in Polynomial Optimization
The SDP (semidefinite programming) relaxation for general POPs (polynomial optimization problems), which was proposed as a method for computing global optimal solutions of POPs by Lasserre, has become an active research subject recently. We propose a new heuristic method exploiting the equality constraints in a given POP, and strengthen the SDP relaxation so as to achieve faster convergence to ...
متن کاملSolving polynomial least squares problems via semidefinite programming relaxations
A polynomial optimization problem whose objective function is represented as a sum of positive and even powers of polynomials, called a polynomial least squares problem, is considered. Methods to transform a polynomial least squares problem to polynomial semidefinite programs to reduce degrees of the polynomials are discussed. Computational efficiency of solving the original polynomial least sq...
متن کاملSums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity
Unconstrained and inequality constrained sparse polynomial optimization problems (POPs) are considered. A correlative sparsity pattern graph is defined to find a certain sparse structure in the objective and constraint polynomials of a POP. Based on this graph, sets of supports for sums of squares (SOS) polynomials that lead to efficient SOS and semidefinite programming (SDP) relaxations are ob...
متن کاملConvergent Relaxations of Polynomial Optimization Problems with Noncommuting Variables
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial inequalities as semidefinite positivity constraints. Such problems arise naturally in quantum theory and quantum information science. To solve them, we intr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2016
ISSN: 1052-6234,1095-7189
DOI: 10.1137/15m1017922