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Deep neural networks (DNNs) can easily be manipulated (by an adversary) to output drastically different predictions and can be done so in a controlled and directed way. This process is known as adversarial attack and is considered one of the major hurdles in using DNNs in high-stakes and real-world applications. Although developing methods to secure DNNs against adversaries is now a primary research focus, it suffers from limitations such as lack of optimization generality and lack of optimization scalability. My research highlights will offer a holistic understanding of optimization foundations for robust AI, peer into their emerging challenges, and present recent solutions developed by my research group.