Titlebook: High Performance Optimization; Hans Frenk,Kees Roos,Shuzhong Zhang Book 2000 Springer Science+Business Media Dordrecht 2000 Finite.algorit

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Self-Dual Embedding Techniquel solutions is known beforehand. We will see in this chapter how we can adapt the algorithms of Chapter 3 to solve semidefinite programming problems without any pre-knowledge. To this end, we use the self-dual embedding technique. This technique will also be used to tackle semidefinite programming p

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Properties of the Central Path will demonstrate that the primal-dual central path converges to the analytic center of the optimal solution set. Moreover, the distance to this analytic center from any point on the central path is shown to converge at the same .-rate as the duality gap. This result can be interpreted as an error-b

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Flatter

The Mosek Interior Point Optimizer for Linear Programming: An Implementation of the Homogeneous Algohomogeneous interior-point algorithm which in contrast to the primal-dual algorithm detects a possible primal or dual infeasibility reliably. It employs advanced (parallelized) linear algebra, it handles dense columns in the constraint matrix efficiently, and it has a basis identification procedure.

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New Complexity Analysis of Primal-Dual Newton Methods for ,,(,) Linear Complementarity Problemswe prove polynomial complexity of the large update method without using a barrier or potential function. Our analysis is based on an appropriate proximity measure only. This proximity measure has not been used in the analysis of a large update method for LCP before. Our new analysis provides a unifi

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Numerical Evaluation of SDPA (Semidefinite Programming Algorithm)the standard form semidefinite program and its dual. We report numerical results of large scale problems to evaluate its performance, and investigate how major time-consuming parts of SDPA vary with the problem size, the number of constraints and the sparsity of data matrices.

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Computational Experience of an Interior-Point SQP Algorithm in a Parallel Branch-and-Bound Frameworkramming relaxations at each node are solved using an interior point SQP method. In contrast to solving the relaxation to optimality at each tree node, the relaxation is only solved to near-optimality. Analogous to employing advanced bases in simplex-based linear MIP solvers, a “dynamic” collection o

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Solving Linear Ordering Problems with a Combined Interior Point/Simplex Cutting Plane Algorithmfew relaxations and then switches to a simplex method to solve the last few relaxations. The simplex method uses CPLEX 4.0. We compare the algorithm with one that uses only an interior point method and with one that uses only a simplex method. We solve integer programming problems with as many as 31

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Finite Element Methods for Solving Parabolic Inverse Problemsm is formulated as a constrained minimization of the ..-norm error between the observation data and the physical solution to the original system, with the ..-regularization or .-regularization. Then the finite element method is used to approximate the constrained minimization problem, and the result