We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions when the stochastic program is expressed in terms of a law invariant coherent risk measure. The obtained results are applied … Read more
The search for a better understanding of complex systems calls for quantitative model development. Within this development process, model fitting to observational data (calibration) often plays an important role. Traditionally, local optimization techniques have been applied to solve nonlinear (as well as linear) model calibration problems numerically: the limitations of such approaches in the nonlinear … Read more
For many Mixed-Integer Programming (MIP) problems, high-quality dual bounds can obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solver, or through Semidefinite Programming (SDP) relaxation hierarchies. In this paper, we introduce an alternative bounding approach that exploits the “combinatorial implosion” effect by solving portions of the original problem and aggregating this information … Read more
The floor layout problem (FLP) tasks a designer with positioning a collection of rectangular boxes on a fixed floor in such a way that minimizes total communication costs between the components. While several mixed integer programming (MIP) formulations for this problem have been developed, it remains extremely challenging from a computational perspective. This work takes … Read more
In this paper we obtained an approach to the optimal switching control problem with unknown switching points which it is described in reference [1, 2]. In reference [1], the authors studied the Decomposition of Linear-Quadratic Optimal Control Problems for Two-Steps Systems. In [1], the authors assumed the switching point t1 is xed in the interval … Read more
We analyze the convergence of stochastic gradient methods for bi-level optimization problems. We address two specific cases: first when the outer objective function can be expressed as a finite sum of independent terms, and next when both the outer and inner objective functions can be expressed as finite sums of independent terms. We assume Lipschitz … Read more
This paper presents an algorithm that solves optimization problems on a matrix manifold $\mathcal{M} \subseteq \mathbb{R}^{m \times n}$ with an additional rank inequality constraint. The algorithm resorts to well-known Riemannian optimization schemes on fixed-rank manifolds, combined with new mechanisms to increase or decrease the rank. The convergence of the algorithm is analyzed and a weighted … Read more
This paper is devoted to the study of unconstrained planar multiobjective location problems, where distances between points are defined by means of the Manhattan norm. By identifying all nonessential objectives, we develop an effective algorithm for generating the whole set of efficient solutions. We prove the correctness of this algorithm and present some computational results, … Read more
We present an online learning approach to variable branching in branch-and-bound for mixed-integer linear problems. Our approach consists in learning strong branching scores in an online fashion and in using them to take branching decisions. More specifically, numerical scores are used to rank the branching candidates. If, for a given variable, the learned approximation is … Read more
Low-rank tensor methods provide efficient representations and computations for high-dimensional problems and are able to break the curse of dimensionality when dealing with systems involving multiple parameters. We present algorithms for constrained nonlinear optimization problems that use low-rank tensors and apply them to optimal control of PDEs with uncertain parameters and to parametrized variational inequalities. … Read more