Silver Lake Management LLC, the biggest technology-focused private-equity firm, will seek to raise $1 billion for a fund focused on mid-sized companies, people with knowledge of the plans said. The new fund, run by the firm’s Silver Lake Sumeru LP unit, will aim for a 2014 debut, said the people, who asked not to be identified because the plans aren’t public. Silver Lake Sumeru, which was introduced in 2008 and raised $1.1 billion, was among the backers of PrimeSense Ltd., the Israeli motion-tracking chipmaker that agreed to be bought by Apple Inc. Silver Lake Management, which was founded in 1999 and manages more than $20 billion in assets, partnered with Michael Dell to buy computer-maker Dell Inc. for $24.9 billion last month. A representative for Menlo Park, California-based Silver Lake declined to comment on the fundraising plans. Silver Lake Sumeru invested $50 million in PrimeSense in 2011, the people said. Apple is buying the Tel Aviv-based company, whose processors let digital devices to detect movement and objects, for about $350 million, one person with knowledge of the deal said last week. Sumeru’s fundraising effort comes as the unit’s founder Ajay Shah is taking a reduced role at the middle-market unit, people with knowledge of the changes have said. This was at least the fourth exit of a Silver Lake Sumeru portfolio company to a strategic buyer. SanDisk Corp. acquired Smart Storage Systems Inc. in August for $307 million. ABB Ltd. bought Power-One Inc., a renewable energy company, in July for about $1 billion. International Business Machines Corp. purchased software-maker i2 Ltd. in 2011 for $500 million.