Many geodetic applications require the minimization of a convex objective function subject to some linear equality and/or inequality constraints. If a system is singular (e.g., a geodetic network without a defined datum) this results in a manifold of solutions. Most state-of-the-art algorithms for inequality constrained optimization (e.g., the Active-Set-Method or primal-dual Interior-Point-Methods) are either not able to deal with a rank-deficient objective function or yield only one of an infinite number of particular solutions.
Roese-Koerner, L., Schuh, W. Convex optimization under inequality constraints in rank-deficient systems. Springer Berlin Heidelberg, 2014 с.415-426,.
Roese-Koerner, L., Schuh, W. Convex optimization under inequality constraints in rank-deficient systems. Springer Berlin Heidelberg, 2014 с.415-426,.
Roese-Koerner, L., Schuh, W. (2014) Convex optimization under inequality constraints in rank-deficient systems, Springer Berlin Heidelberg с.415-426,.
Roese-Koerner, L., & Schuh, W. (2014). Convex optimization under inequality constraints in rank-deficient systems. Springer Berlin Heidelberg, с.415-426.
Roese-Koerner L, Schuh W. Convex optimization under inequality constraints in rank-deficient systems. Springer Berlin Heidelberg; 2014. p. с.415-426.
