The 2-Coordinate Descent Method for Solving Double-Sided Simplex Constrained Minimization Problems

Amir Beck ()
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Amir Beck: Technion—Israel Institute of Technology

Journal of Optimization Theory and Applications, 2014, vol. 162, issue 3, No 12, 892-919

Abstract: Abstract This paper considers the problem of minimizing a continuously differentiable function with a Lipschitz continuous gradient subject to a single linear equality constraint and additional bound constraints on the decision variables. We introduce and analyze several variants of a 2-coordinate descent method: a block descent method that performs an optimization step with respect to only two variables at each iteration. Based on two new optimality measures, we establish convergence to stationarity points for general nonconvex objective functions. In the convex case, when all the variables are lower bounded but not upper bounded, we show that the sequence of function values converges at a sublinear rate. Several illustrative numerical examples demonstrate the effectiveness of the method.

Keywords: Nonconvex optimization; Simplex-type constraints; Block descent method; Rate of convergence (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-013-0491-5

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