We consider the problem of approximating the Pareto set of convex multi-criteria optimization problems by a discrete set of points and their convex combinations. Finding the scalarization parameters that maximize the improvement in bound on the approximation error when generating a single Pareto optimal solution is a nonconvex optimization problem. This problem is solvable by … Read more
It’s shown that a number of variational problems can be cast as finding the maxinf-points (or minsup-points) of bivariate functions, coveniently abbreviated to bifunctions. These variational problems include: linear and nonlinear complementarity problems, fixed points, variational inequalities, inclusions, non-cooperative games, Walras and Nash equilibrium problems. One can then appeal to the theory of lopsided convergence … Read more
In this work, we present new insights into the dynamic stability of electricity markets. In particular, we discuss how short forecast horizons, incomplete gaming, and physical ramping constraints can give rise to stability issues. Using basic concepts of market efficiency, Lyapunov stability, and predictive control, we construct a new stabilizing market design. A numerical case … Read more
In this paper new results are established in multiobjective DC programming with infinite convex constraints ($MOPIC$ for abbr.) that are defined on Banach space (finite or infinite) with objectives given as the difference of convex functions subject to infinite convex constraints. This problem can also be called multiobjective DC semi-infinite and infinite programming, where decision … Read more
Multi-homing is used by Internet Service Provider (ISP) to connect to the Internet via different network providers. This study investigates the optimal routing strategy under multi-homing in the case where network providers charge ISPs according to top-percentile pricing (i.e. based on the $\theta$-th highest volume of traffic shipped). We call this problem the Top-percentile Traffic … Read more
In this paper we study relations between the minimax, risk averse and nested formulations of multistage stochastic programming problems. In particular, we discuss conditions for time consistency of such formulations of stochastic problems. We also describe a connection between law invariant coherent risk measures and the corresponding sets of probability measures in their dual representation. … Read more
We consider the incorporation of a time-consistent coherent risk measure into a multi-stage stochastic programming model, so that the model can be solved using a SDDP-type algorithm. We describe the implementation of this algorithm, and study the solutions it gives for an application of hydro-thermal scheduling in the New Zealand electricity system. The performance of … Read more
We describe experiments with parallel algorithms for computing adaptive controls for attenuating power grid cascading failures. Citation Columbia University, 2010 Article Download View Optimal adaptive control of cascading power grid failures
When solving nonlinear least-squares problems, it is often useful to regularize the problem using a quadratic term, a practice which is especially common in applications arising in inverse calculations. A solution method derived from a trust-region Gauss-Newton algorithm is analyzed for such applications, where, contrary to the standard algorithm, the least-squares subproblem solved at each … Read more
We investigate cost-sharing mechanisms for scheduling cost-sharing games. We assume that the demand is general—that is, each player can be allocated one of several levels of service. We show how to design mechanisms for these games that are weakly group strategyproof, approximately budget-balanced, and approximately efficient, using approximation algorithms for the underlying scheduling problems. We … Read more