Primer approximation multiplex PCR (PAMP) is a new experimental protocol for efficiently assaying structural variation in genomes. PAMP is particularly suited to cancer genomes where the precise breakpoints of alterations such as deletions or translocations vary between patients. The design of PCR primer sets for PAMP is challenging because a large number of primer pairs are required to detect alterations in the hundreds of kilobases range that can occur in cancer. These sets of primers must achieve high coverage of the region of interest, while avoiding primer dimers and satisfying the physico-chemical constraints of good PCR primers. We describe a natural formulation of these constraints as a combinatorial optimization problem. We show that the PAMP primer design problem is NP-hard, and design algorithms based on simulated annealing and integer programming, that provide good solutions to this problem in practice. The algorithms are applied to a test region around the known CDKN2A deletion, which show excellent results even in a 1:49 mixture of mutated:wild-type cells. We use these test results to help set design parameters for larger problems. We can achieve near-optimal designs for regions close to 1 Mb.