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
We present a bundle method for convex nondifferentiable minimization where the model is a piecewise quadratic convex approximation of the objective function. Unlike standard bundle approaches, the model only needs to support the objective function from below at a properly chosen (small) subset of points, as opposed to everywhere. We provide the convergence analysis for … Read more
In this paper we propose an iterative algorithm to solve large size linear inverse ill posed problems. The regularization problem is formulated as a constrained optimization problem. The dual lagrangian problem is iteratively solved to compute an approximate solution. Before starting the iterations, the algorithm computes the necessary smoothing parameters and the error tolerances from … Read more
We consider iterative trust region algorithms for the unconstrained minimization of an objective function F(x) of n variables, when F is differentiable but no derivatives are available, and when each model of F is a linear or quadratic polynomial. The models interpolate F at n+1 points, which defines them uniquely when they are linear polynomials. … Read more
In this note we establish a relation between two bounds for convex maximization problems, the one based on a concavity cut, and the surrogate dual bound. Both bounds have been known in the literature for a few decades but, to the authors’ knowledge, the relation between them has not been previously observed in the literature. … Read more
Combinatorial and logic constraints arising in a number of challenging optimization applications can be formulated as vanishing constraints. Quadratic programs with vanishing constraints (QPVCs) then arise as subproblems during the numerical solution of such problems using algorithms of the Sequential Quadratic Programming type. QPVCs are nonconvex problems violating standard constraint qualifications. In this paper, we … Read more
This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sum-of-squares decomposition to construct a polynomial Lyapunov function. We then show how these methods can be extended … 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
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 1979, L. Lovasz defined the theta number, a spectral/semidefinite upper bound on the stability number of a graph, which has several remarkable properties (e.g. it is exact for perfect graphs). The definition of Lovasz’s theta number relies on the notion of orthonormal representation of the graph, and, dually, can be obtained by optimizing over … Read more