bi-level optimization

Integer Programming Formulations for Minimum Spanning Tree Interdiction

  • Foad Mahdavi Pajou
  • Jose L. Walteros
  • Ningji Wei
    • Categories Branch and Cut Algorithms, Integer Programming, Network Optimization Tags , , ,

    We consider a two-player interdiction problem staged over a graph where the leader’s objective is to minimize the cost of removing edges from the graph so that the follower’s objective, i.e., the weight of a minimum spanning tree in the residual graph, is increased up to a predefined level $r$. Standard approaches for graph interdiction … Read more

    On the convergence of stochastic bi-level gradient methods

  • Nicolas Couellan
  • Wenjuan Wang
    • Categories Data-Mining, Nonlinear Optimization Tags , , ,

    We analyze the convergence of stochastic gradient methods for bi-level optimization problems. We address two specific cases: first when the outer objective function can be expressed as a finite sum of independent terms, and next when both the outer and inner objective functions can be expressed as finite sums of independent terms. We assume Lipschitz … Read more