id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ijassa-1217	Izmailov, Alexey F.; Rodin, Ivan S.	Accelerating Sequential Quadratic Programming for Inequality-Constrained Optimization near Critical Lagrange Multipliers	2022	12	.pdf	application/pdf	5541	337	62	Another source of complications is that the primal part ξk of the NM step vk = (ξk, ηk) computed at the current iterate uk = (xk, λk) can be guaranteed to be a direction of descent for ϕc (with an appropriate choice of c) at uk only provided the Hessian of the Lagrangian Hk = ∂2L ∂x2 (xk, λk) (2.10) is positive definite, which is not at all automatic even close to a solution/multiplier pair satisfying the second-order sufficient optimality condition. QUADRATIC PROGRAMMING FOR INEQUALITY-CONSTRAINED 75 Newton method (NM) defines the next iterate as uk+1 = uk + vk, where vk is a solution of the linearized (at uk) equation Φ(uk) + Φ′(uk)v = 0.	cache/ijassa-1217.pdf	txt/ijassa-1217.txt