Efficiently solving constrained optimization problems is crucial for numerous real-world applications, yet traditional solvers are often computationally prohibitive for real-time use. Machine learning-based approaches have emerged as a promising alternative to provide approximate solutions at faster speeds, but they struggle to strictly enforce constraints, leading to infeasible solutions in practice. To address this, we propose the Feasibility-Seeking Neural Network (FSNet), which integrates a feasibility-seeking step directly into its solution procedure to ensure constraint satisfaction. This feasibility-seeking step solves an unconstrained optimization problem that minimizes constraint violations in a differentiable manner, enabling end-to-end training and providing guarantees on feasibility and convergence. Our experiments across a range of different optimization problems, including both smooth/nonsmooth and convex/nonconvex problems, demonstrate that FSNet can provide feasible solutions with solution quality comparable to (or in some cases better than) traditional solvers, at significantly faster speeds.

Social networks have gained huge research interest, especially in viral marketing due to their rapid boom in the past years. It is very crucial to identify the influential users in the social networks for viral and target marketing. Influence maximization (IM) problem estimates such influential users in the social networks. With an initial seed set, the IM finds a maximum number of nodes that can be activated in the network under some diffusion models e.g. Linear Threshold model or Independent Cascade model. But previous works in this field have not studied about the minimum cost, termed as opportunity cost (OC), to motivate those seed nodes. In this work, we define a novel Reverse Influence Maximization (RIM) problem to determine the opportunity cost of influence maximization. Employing the influence propagation in opposite order, the RIM determines the minimum number of nodes that must be activated in order to motivate a set of target nodes. We propose Random RIM (R-RIM) and Randomized Linear Threshold RIM (RLT-RIM) models to tackle the RIM problem. We also perform a simulation to evaluate the performance of the algorithms using two real world datasets. The result shows that the proposed models determine the optimized opportunity cost with faster running time margin.