Semi-Infinite Programming (SIP) has emerged as a powerful framework for modeling problems with infinite constraints, however, its theoretical development in the context of nonconvex and large-scale optimization remains limited. In this paper, we investigate a class of nonconvex min-max optimization problems with nonconvex infinite constraints, motivated by applications such as adversarial robustness and safety-constrained learning. We propose a novel inexact dynamic barrier primal-dual algorithm and establish its convergence properties. Specifically, under the assumption that the squared infeasibility residual function satisfies the Lojasiewicz inequality with exponent $\theta \in (0,1)$, we prove that the proposed method achieves $\mathcal{O}(\epsilon^{-3})$, $\mathcal{O}(\epsilon^{-6\theta})$, and $\mathcal{O}(\epsilon^{-3\theta/(1-\theta)})$ iteration complexities to achieve an $\epsilon$-approximate stationarity, infeasibility, and complementarity slackness, respectively. Numerical experiments on robust multitask learning with task priority further illustrate the practical effectiveness of the algorithm.

The globalization of the manufacturing process and the supply chain for electronic hardware has been driven by the need to maximize profitability while lowering risk in a technologically advanced silicon sector. However, many hardware IPs’ security features have been broken because of the rise in successful hardware attacks. Existing security efforts frequently ignore numerous dangers in favor of fixing a particular vulnerability. This inspired the development of a unique method that uses emerging spin-based devices to obfuscate circuitry to secure hardware intellectual property (IP) during fabrication and the supply chain. We propose an Optimized and Automated Secure IC (OASIC) Design Flow, a defense-in-depth approach that can minimize overhead while maximizing security. Our EDA tool flow uses a dynamic obfuscation method that employs dynamic lockboxes, which include switch boxes and magnetic random access memory (MRAM)-based look-up tables (LUT) while offering minimal overhead and being flexible and resilient against modern SAT-based attacks and power side-channel attacks. An EDA tool flow for optimized lockbox insertion is also developed to generate SAT-resilient design netlists with the least power and area overhead. PPA metrics and security (SAT attack time) are provided to the designer for each lockbox insertion run. A verification methodology is provided to verify locked and unlocked designs for functional correctness. Finally, we use ISCAS’85 benchmarks to show that the EDA tool flow provides a secure hardware netlist with maximum security while considering power and area constraints. Our results indicate that the proposed OASIC design flow can maximize security while incurring less than 15% area overhead and maintaining a similar power footprint compared to the original design. OASIC design flow demonstrates improved performance as design size increases, which demonstrates the scalability of the proposed approach.

In this paper we propose a class of randomized primal-dual methods incorporating line search to contend with large-scale saddle point (SP) problems defined by a convex-concave function $\mathcal L(\mathbf{x},y) = \sum_{i=1}^M f_i(x_i)+\Phi(\mathbf{x},y)-h(y)$. We analyze the convergence rate of the proposed method under mere convexity and strong convexity assumptions of $\mathcal L$ in $\mathbf{x}$-variable. In particular, assuming $\nabla_y\Phi(\cdot,\cdot)$ is Lipschitz and $\nabla_{\mathbf{x}}\Phi(\cdot,y)$ is coordinate-wise Lipschitz for any fixed $y$, the ergodic sequence generated by the algorithm achieves the $\mathcal O(M/k)$ convergence rate in the expected primal-dual gap. Furthermore, assuming that $\mathcal L(\cdot,y)$ is strongly convex for any $y$, and that $\Phi(\mathbf{x},\cdot)$ is affine for any $\mathbf{x}$, the scheme enjoys a faster rate of $\mathcal O(M/k^2)$ in terms of primal solution suboptimality. We implemented the proposed algorithmic framework to solve kernel matrix learning problem, and tested it against other state-of-the-art first-order methods.

In this paper, we investigate a class of constrained saddle point (SP) problems where the objective function is nonconvex-concave and smooth. This class of problems has wide applicability in machine learning, including robust multi-class classification and dictionary learning. Several projection-based primal-dual methods have been developed to tackle this problem; however, the availability of methods with projection-free oracles remains limited. To address this gap, we propose efficient single-loop projection-free methods reliant on first-order information. In particular, using regularization and nested approximation techniques, we propose a primal-dual conditional gradient method that solely employs linear minimization oracles to handle constraints. Assuming that the constraint set in the maximization is strongly convex, our method achieves an $\epsilon$-stationary solution within $\mathcal{O}(\epsilon^{-6})$ iterations. When the projection onto the constraint set of maximization is easy to compute, we propose a one-sided projection-free method that achieves an $\epsilon$-stationary solution within $\mathcal{O}(\epsilon^{-4})$ iterations. Moreover, we present improved iteration complexities of our methods under a strong concavity assumption. To the best of our knowledge, our proposed algorithms are among the first projection-free methods with convergence guarantees for solving nonconvex-concave SP problems.