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Crash Techniques For LargeScale Complementarity Problems
 COMPLEMENTARITY AND VARIATIONAL PROBLEMS: STATE OF THE ART. SIAM
"... Most Newtonbased solvers for complementarity problems converge rapidly to a solution once they are close to the solution point and the correct active set has been found. We discuss the design and implementation of crash techniques that compute a good active set quickly based on projected gradient a ..."
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Cited by 12 (9 self)
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Most Newtonbased solvers for complementarity problems converge rapidly to a solution once they are close to the solution point and the correct active set has been found. We discuss the design and implementation of crash techniques that compute a good active set quickly based on projected gradient and projected Newton directions. Computational results obtained using these crash techniques with PATH and SMOOTH, stateoftheart complementarity solvers, are given, demonstrating in particular the value of the projected Newton technique in this context.
SENSITIVITY ANALYSIS IN CONVEX QUADRATIC OPTIMIZATION: INVARIANT SUPPORT SET INTERVAL
, 2004
"... In sensitivity analysis one wants to know how the problem and the optimal solutions change under the variation of the input data. We consider the case when variation happens in the right hand side of the constraints and/or in the linear term of the objective function. We are interested to find the r ..."
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Cited by 9 (4 self)
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In sensitivity analysis one wants to know how the problem and the optimal solutions change under the variation of the input data. We consider the case when variation happens in the right hand side of the constraints and/or in the linear term of the objective function. We are interested to find the range of the parameter variation in Convex Quadratic Optimization (CQO) problems where the support set of a given primal optimal solution remains invariant. This question has been first raised in Linear Optimization (LO) and known as Type II (so called Support Set Invariancy) sensitivity analysis. We present computable auxiliary problems to identify the range of parameter variation in support set invariancy sensitivity analysis for CQO. It should be mentioned that all given auxiliary problems are LO problems and can be solved by an interior point method in polynomial time. We also highlight the differences between characteristics of support set invariancy sensitivity analysis for LO and CQO.
A Strongly Polynomial Rounding Procedure Yielding a Maximally Complementary Solution for P*(κ) Linear Complementarity Problems
, 1998
"... We deal with Linear Complementarity Problems (LCPs) with P () matrices. First we establish the convergence rate of the complementary variables along the central path. The central path is parameterized by the barrier parameter , as usual. Our elementary proof reproduces the known result that the var ..."
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Cited by 7 (5 self)
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We deal with Linear Complementarity Problems (LCPs) with P () matrices. First we establish the convergence rate of the complementary variables along the central path. The central path is parameterized by the barrier parameter , as usual. Our elementary proof reproduces the known result that the variables on, or close to the central path fall apart in three classes in which these variables are O(1); O() and O( p ), respectively. The constants hidden in these bounds are expressed in, or bounded by, the input data. All this is preparation for our main result: a strongly polynomial rounding procedure. Given a point with sufficiently small complementarity gap and close enough to the central path, the rounding procedure produces a maximally complementary solution in at most O(n³) arithmetic operations. The result implies that Interior Point Methods (IPMs) not only converge to a complementary solution of P () LCPs but, when furnished with our rounding procedure, they can produce a max...