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We propose a series of new feature weighting algorithms, all stemming from a new interpretation of RELIEF as an online algorithm that solves a convex optimization problem with a margin-based objective function. The new interpretation explains the simplicity and effectiveness of RELIEF, and enables us to identify some of its weaknesses. We offer an analytic solution to mitigate these problems. We extend the newly proposed algorithm to handle multiclass problems by using a new multiclass margin definition. To reduce computational costs, an online learning algorithm is also developed. Convergence theorems of the proposed algorithms are presented. Some experiments based on the UCI and microarray datasets are performed to demonstrate the effectiveness of the proposed algorithms.