Mathematical Programming Study, Volumes 16-18North-Holland Publishing Company, 1982 - Mathematical optimization |
Contents
1 The watchdog technique for forcing convergence in algorithms | 1 |
2 Reduced quasiNewton methods with feasibility improvement | 18 |
3 A superlinearly convergent algorithm for constrained optimization | 45 |
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Common terms and phrases
active set algorithm analysis ap(u applied approximation assume assumption B₁ bounded computational conjugate gradient conjugate gradient methods constrained optimization convex Corollary corresponding defined denote derivatives differentiable equality constraints equation estimate exists finite follows formula given hence Hessian inequality constraints infeasible infimum Jacobian Kuhn-Tucker point Lagrange multipliers Lagrangian Lagrangian function Lemma line search linear constraints linearly constrained Lipschitz continuous Mathematical Programming matrix minimize minimum nonlinear constraints nonlinear programming objective function obtain Operations Research optimal solution optimization problems paper penalty function penalty parameter piecewise smooth function positive definite procedure Proof properties Proposition quadratic programming quasi-Newton method rate of convergence recursive reduced gradient reduced problem satisfies search direction Section sequence smooth functions solving Step stochastic structure subproblem subset superbasic Theorem theory University update variables vector xk+1 zero Zk+1