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|Title:||Global linear and local quadratic convergence of a long-step adaptive-mode interior point method for some monotone variational inequality problems|
|Authors:||Sun, J. |
|Keywords:||Interior point methods|
Monotone variational inequality problems
Polynomial complexity of algorithms
Rate of convergence
|Source:||Sun, J.,Zhao, G. (1998). Global linear and local quadratic convergence of a long-step adaptive-mode interior point method for some monotone variational inequality problems. SIAM Journal on Optimization 8 (1) : 123-139. ScholarBank@NUS Repository.|
|Abstract:||An interior point (IP) method is proposed to solve variational inequality problems for monotone functions and polyhedral sets. The method has the following advantages: 1. Given an initial interior feasible solution with duality gap μ0, the algorithm requires at most O[n log(μ0/ε)] iterations to obtain an ε-optimal solution. 2. The rate of convergence of the duality gap is q-quadratic. 3. At each iteration, a long-step improvement is allowed. 4. The algorithm can automatically transfer from a linear mode to a quadratic mode to accelerate the local convergence.|
|Source Title:||SIAM Journal on Optimization|
|Appears in Collections:||Staff Publications|
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