Abstract We consider the optimistic bilevel optimization problem, known to have a wide range of applications in engineering, that we transform into single-level problem by means lower-level optimal value function reformulation. Subsequently, based on partial calmness concept, build an equation system, which is parameterized corresponding exact penalization parameter. then design and analyze Lev...

We use a primal-dual scheme to devise a new update rule for a penalty function method applicable to general optimization problems, including nonsmooth and nonconvex ones. The update rule we introduce uses dual information in a simple way. Numerical test problems show that our update rule has certain advantages over the classical one. We study the relationship between exact penalty parameters an...

Many least-square problems involve affine equality and inequality constraints. Although there are a variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current article proposes a new path-following algorithm for quadratic programming that replaces hard constraints by what are called exact penalties. Similar penalties arise in l1 regulari...

EQUALITY CONSTRAINED OPTIMIZATION Masao Fukushima Kyoto University Hisashi Mine Kansai University Eiki Yamakawa Kyoto University (Received November 12, 1984: Revised June 12, 1985) This paper is concerned with a differentiable exact penalty function derived by modifying the Wolfe dual of an equality constrained problem. It may be considered that this penalty function belongs to a class of gener...

Given a graph G and a positive integer k, we want to nd k spanning trees on G, not necessarily disjoint, of minimum total weight, such that the weight of each edge is subject to a penalty function if it belongs to more than one tree. We present a polynomial time algorithm for this problem; the algorithm's complexity is quadratic in k. We also present two heuristics with complexity linear in k. ...