The event invites WTA tournament winners from the current calendar year who didn't qualify for the WTA Championships. Halep won five titles this year, second only to world No. 1 Serena Williams, who notched her 11th win of the year Sunday in the WTA Championships final.
Halep had little trouble in disposing of sixth-seeded Anastasia Pavlyuchenkova 6-3, 6-3 in 68 minutes in her first Group A match in Sofia.
Halep finished with five breaks. Three of those came in the first set when she set the tone of the match by winning 55 percent of the points.
Ivanovic, seeded second, grabbed the early lead in Group B with a 6-0, 6-2 win over No. 8-seeded Tsvetana Pironkova in 55 minutes. Ivanovic dropped just 10 points on serve and allowed Pironkova just 14 when receiving.
Cornet, the No. 7-seed, jumped out to a 5-0 lead when third-seeded Maria Kirilenko retired with an injury. Elina Svitolina will take Kirilenko's spot in Group A.
The two other players in Group B -- Samantha Stosur and Elena Vesnina -- will meet in their first match of round-robin play Wednesday. Also Halep takes on Cornet and Svitolina meets Pavlyuchenkova in Group A matches.
The two top players in each group advance to the tournament semifinals Saturday.