The Nelson-Siegel and the Svensson models are two of the most widely used models for the term structure of interest rates. Even though the models are quite simple and intuitive, fitting them to market data is numerically challenging and various difficulties have been reported. In this paper, a novel mathematical analysis of the fitting problem … Read more
We describe a parametric univariate quadratic optimization problem for which the moment-SOS hierarchy has finite but increasingly slow convergence when the parameter tends to its limit value. We estimate the order of finite convergence as a function of the parameter. ArticleDownload View PDF
The central challenges of today’s neural network architectures are the prohibitive memory footprint and training costs associated with determining optimal weights and biases. A large portion of research in machine learning is therefore dedicated to constructing memory-efficient training methods. One promising approach is dynamical low-rank training (DLRT), which represents and trains parameters as a low-rank … Read more
We develop a new approximation theory for linear and quadratic interpolation models, suitable for use in convex-constrained derivative-free optimization (DFO). Most existing model-based DFO methods for constrained problems assume the ability to construct sufficiently accurate approximations via interpolation, but the standard notions of accuracy (designed for unconstrained problems) may not be achievable by only sampling … Read more
This paper presents a unified approach for maximizing continuous \(\gamma\)-weakly DR-submodular functions that encompasses a range of settings and oracle access types. Our approach includes a Frank-Wolfe type offline algorithm for both monotone and non-monotone functions, with different restrictions on the convex feasible region. We consider settings where the oracle provides access to either the … Read more
Abstract: In a real Hilbert space domain setting, we study the convergence properties of the stochastic Ravine accelerated gradient method for convex differentiable optimization. We consider the general form of this algorithm where the extrapolation coefficients can vary with each iteration, and where the evaluation of the gradient is subject to random errors. This general … Read more
A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton’s method to the system obtained by the corresponding first-order necessary optimality conditions. However, when taking into account the game dynamics, it is not clear what is the goal of each player when considering they are taking their current … Read more
We introduce a polyhedral framework for characterizing instances of quadratic combinatorial optimization programs (QCOPs) as being linearizable, meaning that the quadratic objective can be equivalently rewritten as linear in such a manner that preserves the objective function value at all feasible solutions. In particular, we show that an instance is linearizable if and only if … Read more
A multiobjective stochastic convex quadratic program (MOSCQP) is a multiobjective optimization problem with convex quadratic objectives that are observed with stochastic error. MOSCQP is a useful problem formulation arising, for example, in model calibration and nonlinear system identification when a single regression model combines data from multiple distinct sources, resulting in a multiobjective least squares … Read more
Existing decentralized algorithms usually require knowledge of problem parameters for updating local iterates. For example, the hyperparameters (such as learning rate) usually require the knowledge of Lipschitz constant of the global gradient or topological information of the communication networks, which are usually not accessible in practice. In this paper, we propose D-NASA, the first algorithm … Read more