2 citations · 4 across the 3 of their papers we have counts for
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Finding Nonlinear Production -- Consumption Equilibrium
Roman Polyak
We introduce and study nonlinear production - consumption equilibrium (NPCE). The NPCE is a combination and generalization of both classical linear programming (LP) and classical i…
Exterior Distance Function
Roman Polyak
We introduce and study exterior distance function (EDF) and correspondent exterior point method (EPM) for convex optimization. The EDF is a classical Lagrangian for an equivalent p…
Complexity of the Regularized Newton Method
Roman Polyak
Newton's method for finding an unconstrained minimizer for strictly convex functions, generally speaking, does not converge from any starting point. We introduce and study the damp…
The Legendre Transform in Modern Optimization
Roman Polyak
The Legendre transform (LET) is a product of a general duality principle: any smooth curve is, on the one hand, a locus of pairs, which satisfy the given equation and, on the other…