Under pressure from an activist shareholder, General Electric Co.’s board has agreed to more closely link the bonuses of its executive management team to the performance of the company’s industrial operations.

Boston-based GE said on Wednesday that the board made the changes following talks with Trian Fund Management, an investment firm led by Nelson Peltz. Trian currently controls a nearly 1 percent stake in GE.

Top executives, including GE chief executive Jeff Immelt and many of the executives he oversees directly, would see their bonuses grow by 20 percent if the company meets both operating profit and structural cost reduction targets for its industrial operations. If the company falls short of both goals, the bonuses would drop 20 percent. If GE hits just one of the two goals, bonuses would remain untouched.

GE said it is reducing expenses in its industrial operations by $1 billion to $23.9 billion in 2017. (GE also set a target for an industrial profit of $17.2 billion this year, essentially flat from last year.) The company aims to take another $1 billion out of costs in 2018.

A spokeswoman for GE declined to comment beyond the description of the changes that the company filed with the Securities and Exchange Commission.

Under Immelt’s leadership, GE has largely exited its financial services businesses and has instead focused on industrial work. The industrial operations targeted in Wednesday’s statement represented roughly 90 percent of the company’s revenue last year.

Fox Business reported earlier this month that Trian had become frustrated with Immelt’s leadership, particularly with his inability to make substantive budget cuts of the size Trian would like to see. Citing anonymous sources, Fox Business said Peltz and his team were considering whether they should push for Immelt to retire early. Immelt, who has been CEO since 2001, has not set a retirement date.

GE’s stock is down 4.9 percent in the past year, compared with a gain of 15 percent by the Standard & Poor’s 500. It closed Wednesday at $29.53, up 0.48 percent.

Trian issued a statement on Wednesday saying that it is pleased with GE’s new approach and that Trian’s management believes the changes to the senior GE executives’ compensation packages are positive for shareholders. “We will continue to hold management accountable to its commitments,’’ the firm said in the statement.

$1 billion

Amount GE said it is reducing expenses in its industrial operations, to $23.9 billion in 2017. The company also has set a target for an industrial profit of $17.2 billion this year, essentially the same as last year.

Jon Chesto can be reached at jon.chesto@globe.com. Follow him on Twitter @jonchesto.