Article,
Solving sparse polynomial optimization problems with chordal structure using the sparse bounded-degree sum-of-squares hierarchy
Affiliations
- [1] Eindhoven University of Technology [NORA names: Netherlands; Europe, EU; OECD];
- [2] Delft University of Technology [NORA names: Netherlands; Europe, EU; OECD];
- [3] Tilburg University [NORA names: Netherlands; Europe, EU; OECD];
- [4] MOSEK ApS, Copenhagen O, Denmark [NORA names: Other Companies; Private Research; Denmark; Europe, EU; Nordic; OECD]
Abstract
The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser et al. (2017) constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proved by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality constraints directly, without eliminating or replacing them by two inequalities. We also evaluate the sparse-BSOS hierarchy on a well-known bilinear programming problem, called the pooling problem, as well as a discrete-time optimal control problem.
Keywords
Weisser,
assumptions,
authors,
bilinear programming problem,
bounds,
chordal structure,
constraints,
construction,
control problem,
discrete-time optimal control problem,
equality,
equality constraints,
hierarchy,
inequality,
lower bounds,
optimal control problem,
optimal value,
pool,
pooling problem,
problem,
programming problem,
sequence,
sequence of lower bounds,
structure,
values