The classical trust-region subproblem (TRS) minimizes a nonconvex quadratic objective over the unit ball. In this paper, we consider extensions of TRS having extra constraints. When two parallel cuts are added to TRS, we show that the resulting nonconvex problem has an exact representation as a semidefinite program with additional linear and second-order-cone constraints. For … Read more
Accurate measurements of snow water equivalent (SWE) is an important factor in managing water resources for hydroelectric power generation. SWE over a catchment area may be estimated via kriging on measures obtained by snow monitoring devices positioned at strategic locations. The question studied in this paper is to find the device locations that minimize the … Read more
We consider a derivative-free optimization, and in particular black box optimization, where the functions to be minimized and the functions representing the constraints are given by black boxes without derivatives. Two fundamental families of methods are available: model-based methods and directional direct search algorithms. This work exploits the flexibility of the second type of methods … Read more
An optimal planning of future wireless networks is fundamental to satisfy rising traffic demands jointly with the utilization of sophisticated techniques, such as OFDMA. Current methods for this task require a static model of the problem. However, uncertainty of data arises frequently in wireless networks, e. g., fluctuat- ing bit rate requirements. In this paper, … Read more
In this paper, we propose a chance-constrained mathematical program for fixed broadband wireless networks under unreliable channel conditions. The model is reformulated as integer linear program and valid inequalities are derived for the corresponding polytope. Computational results show that by an exact separation approach the optimality gap is closed by 42 % on average. Article … Read more
While semidefinite relaxations are known to deliver good approximations for combinatorial optimization problems like graph bisection, their practical scope is mostly associated with small dense instances. For large sparse instances, cutting plane techniques are considered the method of choice. These are also applicable for semidefinite relaxations via the spectral bundle method, which allows to exploit … Read more
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate of the radius of the convergence ball. Some applications for solving constrained nonlinear equations are discussed and the numerical performance of … Read more
Hierarchies of semidefinite programs have been used to approximate or even solve polynomial programs. This approach rapidly becomes computationally expensive and is often tractable only for problems of small size. In this paper, we propose a dynamic inequality generation scheme to generate valid polynomial inequalities for general polynomial programs. When used iteratively, this scheme improves … Read more
In this paper, we study 0-1 mixed-integer bilinear covering sets. We derive several families of facet-defining inequalities via sequence-independent lifting techniques. We then show that these sets have polyhedral structures that are similar to those of certain fixed-charge single-node flow sets. As a result, we obtain new facet-defining inequalities for these sets that generalize well-known … Read more
We present a single sufficient condition for the processability of the Lemke algorithm for semimonotone Linear Complementarity problems (LCP) which unifies several sufficient conditions for a number of well known subclasses of semimonotone LCPs. In particular, we study the close relationship of these problems to the complexity class PPAD. Next, we show that these classes … Read more