This paper proposes an algorithm, RMDA, for training neural networks (NNs) with a regularization term for promoting desired structures. RMDA does not incur computation additional to proximal SGD with momentum, and achieves variance reduction without requiring the objective function to be of the finite-sum form. Through the tool of manifold identification from nonlinear optimization, we … Read more
In this paper we consider the solution of optimization tasks with a piecewise linear objective function and piecewise linear constraints. First, we state optimality conditions for that class of problems using the abs-linearization approach and prove that they can be verified in polynomial time. Subsequently, we propose an algorithm called Constrained Active Signature Method that … Read more
We study a two-stage, finite-scenarios stochastic version of the set multicover problem, where there is uncertainty about a demand for each element to be covered and the penalty cost is imposed linearly on the shortfall in each demand. This problem is NP-hard and has an application in shift scheduling in crowdsourced delivery services. For this … Read more
We consider the problem of a storage owner who trades in a multi-settlement electricity market comprising an auction-based day-ahead market and a continuous intraday market. We show in a stylized model that a coordinated policy that reserves capacity for the intraday market is optimal and that the gap to a sequential policy increases with intraday … Read more
Let S be a compact semialgebraic set and let f be a polynomial nonnegative on S. Schmüdgen’s Positivstellensatz then states that for any \eta>0, the nonnegativity of f+\eta on S can be certified by expressing f+\eta as a conic combination of products of the polynomials that occur in the inequalities defining S, where the coefficients … Read more
Given a grid of active and inactive pixels, the weighted rectangles partitioning (WRP) problem is to find a maximum-weight partition of the active pixels into rectangles. WRP is formulated as an integer programming problem and instances with an integral relaxation polyhedron are characterized by a balanced problem matrix. A complete characterization of these balanced instances … Read more
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is smooth at every iterate, the corresponding local models are unstable and the number of cutting planes invoked by traditional remedies is … Read more
This paper studies construction of signals, which are sparse or nearly sparse with respect to a tight frame $D$ from underdetermined linear systems. In the paper, we propose a non-convex relaxed $\ell_q(0 ArticleDownload View PDF
A compact operations research (OR) model is proposed to analyse the prospects of meeting the Paris Agreement targets when direct air capture technologies can be used or not. The main features of the model are (i) the representation of the economy and energy use with a nested constant elasticity of substitution production function; (ii) the … Read more
We introduce a novel incremental network design problem motivated by the expansion of hub capacities in package express service networks: the \textit{incremental network design problem with multi-commodity flows}. We are given an initial and a target service network design, defined by a set of nodes, arcs, and origin-destination demands (commodities), and we seek to find … Read more