Ana Ivanovic and Simona Halep cruised to straight-set victories in Sofia on Tuesday in their opening round-robin matches at the season-ending Tournament of Champions.

Top-seeded Halep of Romania defeated Russia’s Anastasia Pavlyuchenkova 6-3 6-3 in the Serdika group, while the other tournament favourite, Ivanovic, routed Bulgaria’s Tsvetana Pironkova 6-0 6-2 in the Sredets group.

In Tuesday’s third match, third-seeded Maria Kirilenko retired due to injury against France’s Alize Cornet, and had to quit the tournament for a second consecutive year.

Cornet was leading 5-0 in the first when Kirilenko called for a medical time out, before later abandoning the competition.

Ukraine’s Elina Svitolina will replace Kirilenko.

Samantha Stosur starts her Tournament of Champions campaign on Wednesday morning in Bulgaria (8pm AEDT Wednesday).