• Interior-point and path-following frameworks unify primal-dual strategies, barrier-based updates, and predictor-corrector variants to solve linear and convex programs with strong convergence guarantees [10], [9], [1], [2], [7], [3].

• Decomposition, projection-based and convex-feasibility methods enable scalable optimization via projective/decomposition algorithms, interpretations of parallel projections, gradient-projection variants, and cutting-plane ideas for semi-infinite problems [6], [12], [14], [4].

• Matrix- and eigenvalue-oriented convex optimization leverages interior-point ideas to minimize spectral quantities, including maximum eigenvalue problems, eigenvalue perturbations, and semidefinite-relaxation views [5], [11], [13].

• Nonconvex/non-smooth and parametric optimization analyses address local minimizers, convergence properties, and sensitivity under cone constraints, exploring rank-two structures, nondifferentiability, and essentially smooth landscapes [8], [16], [17], [18], [19], [15].