Multidimensional Approximation Algorithms for Capacity-Expansion Problems

An Approximation Scheme for Stochastic Integer Programs Arising in Capacity Expansion

Planning for capacity expansion forms a crucial part of the strategic level decision making in many applications. Consequently, quantitative models for economic capacity expansion planning have been the subject of intense research. However, much of the work in this area has been restricted to linear cost models and/or limited degree of uncertainty to make the problems analytically tractable. Th...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

Optimal Convergence Rate of the Randomized Algorithms of Stochastic Approximation in Arbitrary Noise

Multidimensional stochastic optimization plays an important role in analysis and control of many technical systems. To solve the challenging multidimensional problems of optimization, it was suggested to use the randomized algorithms of stochastic approximation with perturbed input which are not just simple, but also provide consistent estimates of the unknown parameters for observations in “al...

Approximation Solutions for Time-Varying Shortest Path Problem

Abstract. Time-varying network optimization problems have tradition-ally been solved by specialized algorithms. These algorithms have NP-complement time complexity. This paper considers the time-varying short-est path problem, in which can be optimally solved in O(T(m + n)) time,where T is a given integer. For this problem with arbitrary waiting times,we propose an approximation algorithm, whic...

A Hybrid Approach for the 01 Multidimensional Knapsack problem

& is called a knapsack constraint. The special case of the MKP01 with %*!) is the classical knapsack problem (KP01), whose usual statement is the following. Given a knapsack of capacity and objects, each being associated a profit (gain) and a volume occupation, one wants to select + ( +, and + not fixed) objects such that the total profit is maximized and the capacity of the knapsack is not exc...