By Jong-Shi Pang (auth.), Jong-Shi Pang (eds.)

ISBN-10: 1461373670

ISBN-13: 9781461373674

ISBN-10: 1461551978

ISBN-13: 9781461551973

Computational Optimization: A Tribute to Olvi Mangasarian serves as an exceptional reference, delivering perception into one of the most not easy study matters within the box.
This choice of papers covers a large spectrum of computational optimization issues, representing a mix of universal nonlinear programming themes and such novel paradigms as semidefinite programming and complementarity-constrained nonlinear courses. Many new effects are awarded in those papers that are certain to motivate extra learn and generate new avenues for functions. an off-the-cuff categorization of the papers contains:

  • Algorithmic advances for unique periods of restricted optimization difficulties
  • Analysis of linear and nonlinear courses
  • Algorithmic advances
  • B- desk bound issues of mathematical courses with equilibrium constraints
  • Applications of optimization
  • Some mathematical themes
  • Systems of nonlinear equations.

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Read e-book online Computational Optimization: A Tribute to Olvi Mangasarian PDF

Computational Optimization: A Tribute to Olvi Mangasarian serves as a superb reference, delivering perception into the most hard examine matters within the box. This selection of papers covers a large spectrum of computational optimization themes, representing a mix of widespread nonlinear programming themes and such novel paradigms as semidefinite programming and complementarity-constrained nonlinear courses.

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Extra info for Computational Optimization: A Tribute to Olvi Mangasarian Volume I

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Pp. 75-110. 7. W. Li, "Abadie's constraint qualification. metric regularity. and error bounds for differentiable convex inequalities," SIAM J. on Optimization. vol. 7. pp. 966-978,1997. 8. -D. -Q. Luo. "Extension of HotTman's error bound to polynomial systems," SIAM J. on Optimization, vol. 4, pp. 383-392,1994. 9. -Q. Luo and P. Tseng. "Error bound and convergence analysis of matrix splitting algorithms for the affine variational inequality problem," SIAM 1. on Optimization, vol. 2, pp. 43-54, 1992.

3. Proof of Propositions 1 and 2 We consider the subset of ~W+ I A = fez, w) I there exists x E X such that g(x) ::s z, f(x) ::s w}, and its convex hull Conv(A). The vectors (g(XF). f(xd) and (g(x/), f(x[) belong to A. /), where j = inf{w I (z, w) E Conv(A)}. 50 BERTSEKAS is in the closure of Conv(A). Let us now show that q* S j, as indicated by figure l. (XI) + ~d(X2) S ~I g(XI) Z, W. (X2) + fl'g(X2). (XI) Combining the preceding four inequalities, we obtain q(fl) S W + fl'z, V(z, W) E Conv(A), fl::: O.

The article of Olvi on the condition number for differentiable functions. P. Crouzeix and myself to study sharp error bounds and develop the notion of well behaved asymptotic functions. Likewise. the paper of Chen and Mangasarian on smoothing methods for complementarity. motivated a work by Cominetli. Haddou and myself which allowed us to deepen the role of recession functions in numerical methods for optimization problems. It has been always fruitful for me to read the works of Olvi. and I am delighted to contribute to this volume in honor of Olvi Mangasarian 65th birthday.

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Computational Optimization: A Tribute to Olvi Mangasarian Volume I by Jong-Shi Pang (auth.), Jong-Shi Pang (eds.)


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