The biggest proxy fight against a company has begun, and it's Procter & Gamble against Nelson Peltz. Mr. Peltz's Trian unveiled a board challenge on Monday at the consumer products giant, the biggest company by market capitalization to face a formal proxy fight, highlighting the continued power of shareholder activism in the corporate world. Procter & Gamble had already rejected a demand from Trian to make Mr. Peltz a director, according to The Wall Street Journal, which first reported Trian's plans. The investment firm owns roughly $3.3 billion worth of Procter & Gamble stock. The company has experienced sluggish sales growth and it had been under pressure from another activist investor, William A. Ackman.