Abstract
We propose a new method for equality constrained optimization based on augmented Lagrangian method. We construct an unconstrained subproblem by adding an adaptive quadratic term to the quadratic model of augmented Lagrangian function. In each iteration, we solve this unconstrained subproblem to obtain the trial step. The main feature of this work is that the subproblem can be more easily solved. Numerical results show that this method is effective.
Highlights
IntroductionWe consider the following equality constrained optimization: min f (x) (1)
In this paper, we consider the following equality constrained optimization: min f (x) (1)s.t. ci (x) = 0, i = 1, . . . , m, where x ∈ Rn, f(x) : Rn → R, and ci(x) : Rn → R (i = 1, . . . , m) are twice continuously differentiable.The method presented in this paper is a variant of the augmented Lagrangian method
We propose a new method for equality constrained optimization based on augmented Lagrangian method
Summary
We consider the following equality constrained optimization: min f (x) (1). Later Conn et al [3, 4] presented a practical AL method and proved the global convergence under the LICQ condition. In a typical AL method, at the kth step, for given multiplier λk and penalty parameter σk, an unconstrained subproblem min x∈Rn. is solved to find the iteration point. At the kth step of our algorithm, we solve the following convex unconstrained quadratic subproblem: min s∈Rn mk (10). When ρk is close to zero, we set xk+1 = xk and increase the value of μk, by which we wish to reduce the length of the trial step This technique is similar to the update rule of trust region radius. M} maintains constant rank in a neighborhood of x; RCR is equivalent to RCPLD in which {∇ci(x) | i = 1, . Λ(i) denotes the ith component of the vector λ
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