We study the problem of finding a minimum weight connected subgraph spanning at least k vertices on planar, node-weighted graphs. We give a (4 + ε)-approximation algorithm for this problem. In the process, we use the recent LMP primal-dual 3-approximation for the node-weighted prize-collecting Steiner tree problem [4] and the Lagrangian relaxation [6]. In particular, we improve the procedure of...

Unit commitment (UC) is to determine the optimal unit status and generation level during each time interval of the scheduled period. The purpose of UC is to minimize the total generation cost while satisfying system demand, reserve requirements, and unit constraints. Among the UC constraints, an adequate provision of reserve is important to ensure the security of power system and the fast-respo...

This paper proposes an optimal algorithm for distributed orbit determination by using discrete observations provided from multiple tracking stations in a connected network. The objective is to increase the precision of estimation by communication and cooperation between tracking stations in the network. We focus on the dynamical approach considering a simplified Low Earth Orbital Satellite mode...

Maximum a-posteriori (MAP) estimation is an important task in many applications of probabilistic graphical models. Although finding an exact solution is generally intractable, approximations based on linear programming (LP) relaxation often provide good approximate solutions. In this paper we present an algorithm for solving the LP relaxation optimization problem. In order to overcome the lack ...

We present methods for constructing approximation algorithms to NP-hard optimization problems using linear programming (LP). We typically obtain an LP relaxation of the problem by formulating it as an integer linear program and dropping the integrality constraints. We then solve the LP relaxation exactly, and apply various rounding strategies (including randomized rounding and iterative roundin...

in this paper mathematical structure of time-dependent lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent lagrangian systems are considered. starting point is time-independent lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to the...

This paper is devoted to the numerical resolution of unit-commitment problems. More precisely we present the French model optimizing the daily production of electricity. Its resolution is done is two phases: first a Lagrangian relaxation solves the dual to find a lower bound; it also gives a primal relaxed solution. The latter is used in the second phase for a heuristic resolution based on a pr...

Due to its relatively high total energy eeciency, the application of cogeneration is attracting increased attention. Today cogeneration is an essential element in the energy supply system in many countries, and when environmental and economic aspects are considered too, it seems to be a relevant option in expansion planning in many situations. The present paper presents a quite general and yet ...

ABSTRACT: We consider a two-level lot-sizing problem where the first level consists of N end products competing for a single type of raw material (second level), which is supposed to be critical. In particular, the storage capacity of raw materials is limited and must be carefully managed. The goal is to simultaneously determine an optimal replenishment plan for the raw material and optimal pro...

We develop an algorithm for the linear ordering problem, which has a large number of applications such as triangulation of input-output matrices, minimizing total weighted completion time in one-machine scheduling, and aggregation of individual preferences. The algorithm is based on the Lagrangian relaxation of a binary integer linear programming formulation of the problem. Since the number of ...