Sparse projections onto the simplex
نویسندگان
چکیده
Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the `1-norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank and sparsity constraints. In this setting, we derive efficient sparse projections onto the simplex and its extension, and illustrate how to use them to solve high-dimensional learning problems in quantum tomography, sparse density estimation and portfolio selection with non-convex constraints.
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A deficient-basis dual counterpart of Paparrizos, Samaras and Stephanides' primal-dual simplex-type algorithm
In a recent primal-dual simplex-type algorithm [K. Paparrizos, N. Samaras and G. Stephanides, 2003, A new efficient primal dual simplex algorithm. Computers & Operations Research 30, 1383–1399], their authors show how to take advantage of the knowledge of a primal feasible point and they work with a square basis during the whole process. In this paper we address what could be thought of as its ...
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