Related papers: Consistency Cuts for Dantzig-Wolfe Reformulations
The mixing set with a knapsack constraint arises as a substructure in mixed-integer programming reformulations of chance-constrained programs with stochastic right-hand-sides over a finite discrete distribution. Recently, Luedtke et al.…
This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…
This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…
By introducing a quadratic perturbation to the canonical dual of the maxcut problem, we transform the integer programming problem into a concave maximization problem over a convex positive domain under some circumstances, which can be…
The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
LSTD is a popular algorithm for value function approximation. Whenever the number of features is larger than the number of samples, it must be paired with some form of regularization. In particular, L1-regularization methods tend to perform…
Variational inequalities are an important tool, which includes minimization, saddles, games, fixed-point problems. Modern large-scale and computationally expensive practical applications make distributed methods for solving these problems…
We consider a problem concerning a network and a set of maintenance requests to be undertaken. We wish to schedule the maintenance in such a way as to minimise the impact on the total throughput of the network. We apply disaggregated…
In this paper, for the first time in the literature, we study the stability of solutions of two classes of feasibility (i.e., split equality and split feasibility) problems by set-valued and variational analysis techniques. Our idea is to…
This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…
Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous…
We consider regularized cutting-plane methods to minimize a convex function that is the sum of a large number of component functions. One important example is the dual problem obtained from Lagrangian relaxation on a decomposable problem.…
Local consistency techniques such as k-consistency are a key component of specialised solvers for constraint satisfaction problems. In this paper we show that the power of using k-consistency techniques on a constraint satisfaction problem…
Stiff and chaotic differential equations are challenging for time-stepping numerical methods. For explicit methods, the required time step resolution significantly exceeds the resolution associated with the smoothness of the exact solution…
We consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-cuts) that defines the convex hull of the integer…
The Sequential Multiple Knapsack Problem is a special case of Multiple knapsack problem in which the items sizes are divisible. A characterization of the optimal solutions of the problem and a description of the convex hull of all the…
Our recent study (Lin and Ohtsuka, 2024) proposed a new penalty method for solving mathematical programming with complementarity constraints (MPCC). This method first reformulates MPCC as a parameterized nonlinear programming called gap…
We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale…