M. H. Wright. The interior-pointrevolution in constrained optimization. In R. DeLeone, A. Murli, P.M.Pardalos, and G. Toraldo, editors, HighPerformance Algorithms and Software in Nonlinear Optimization, pages 359--381. Kluwer Academic Publishers, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....counterpart, the past couple of decades has witnessed a tremendous amountofresearchindevelopment of effifi t algorithms for solving nonlinear programs. Several interior point methods have been developed for solution of quadratic programing problems which are a special class of nonlinear programs [Wri98] General nonlinear programing problems can be solved by finding the solution to a sequence of quadratic programs using a method known as sequential quadratic programing [GMSW98] Both linear and nonlinear programing, however, are static optimization problems. An interesting and useful class of ....

M. H. Wright. The interior-pointrevolution in constrained optimization. In R. DeLeone, A. Murli, P.M.Pardalos, and G. Toraldo, editors, HighPerformance Algorithms and Software in Nonlinear Optimization, pages 359--381. Kluwer Academic Publishers, 1998.

....by Khachiyan was an interior point algorithm, meaning that it produced points in the relative interior of the feasible region. Although the theoretical, worstcase complexity of this algorithm was provably superior to that of the simplex algorithm, implementation showed no such realistic advantage [91]. This was not the rst interior point algorithm presented for linear programming. In 1967, Huard [36] suggested using a method of centers to solve mathematical programs problems. Even though Huard proved that these algorithms converge to an optimal solution, the success of Dantzig s simplex method ....

M. Wright. The interior-point revolution in constrained optimization. Technical Report 98-4-09, Bell Laboratories, Murray Hill, New Jersey, 1998.

....function is (x; def = f(x) p X i=1 log c i (x) 1. 3) where the functions c i ( are the components of the vector function c( Once an (approximate) solution x k 1 of BS( k ) is found, the parameter k is updated and attention turns to the next barrier subproblem (see for instance [6, 16, 18] for a general survey and [19] for the linear case) Under reasonable conditions [2, 6, 16] it can be shown that the sequence fx k g converges to a stationary point x of NLP. A typical stopping criterion for the solution of BS( is kP N (A) r x (x; k #( 1.4) where P N (A) is the ....

M. H. Wright. The interior-point revolution in constrained optimization. Technical Report 98-4-09, Computing Sciences Research Center, Bell Laboratories, Murray Hill, New Jersey 07974, June 1998.

....( 23] 71] No established implementation of penalty or barrier methods exists to date. In the last few years there has been intensive research in the development of interior point methods for nonlinear programming ( 79] 3] 1] 2] 20] 47] 78] 12] 31] 70] 74] 82] 76] [80]) Several promising new algorithms have been proposed, and are being developed into high quality software ( 77] 12] 84] Not surprisingly, these algorithms make use of many of the mechanisms employed in established algorithms to enforce convergence from remote starting points and to deal ....

M. H. Wright. The interior-point revolution in constrained optimization. Technical Report 98-4-09, Computing Sciences Research Center, Bell Laboratories, Murray Hill, New Jersey 07974, USA, June 1998.

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M.H. Wright (1998). "The Interior-Point Revolution in Constrained Optimization". Technical Report 98-4-09. Computing Sciences Research Center Bell Laboratories, Murray Hill, New Jersey.

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