Related papers: Computing D-Optimal solutions for huge-scale linea…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
In the big data era researchers face a series of problems. Even standard approaches/methodologies, like linear regression, can be difficult or problematic with huge volumes of data. Traditional approaches for regression in big datasets may…
We develop $D$-optimal designs for linear main effects models on a subset of the $2^K$ full factorial design region, when the number of factors set to the higher level is bounded. It turns out that in the case of narrow margins only those…
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…
We develop algorithms capable of tackling robust black-box optimisation problems, where the number of model runs is limited. When a desired solution cannot be implemented exactly the aim is to find a robust one, where the worst case in an…
We develop a branch-and-bound algorithm for the integer D-optimality problem, a central problem in statistical design theory, based on two convex relaxations, employing variable-bound tightening and fast local-search procedures, testing our…
The topic of learning to solve optimization problems has received interest from both the operations research and machine learning communities. In this work, we combine techniques from both fields to address the problem of learning to…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
In this paper we focus on the unconstrained binary quadratic optimization model, maximize x^t Qx, x binary, and consider the problem of identifying optimal solutions that are robust with respect to perturbations in the Q matrix.. We are…
We provide a systematic treatment of $D$-optimal design for binary regression and quantal response models in toxicology studies. For the two-parameter case, we provide an analytical equation (WC equation) for computing the $D$-optimal…
We develop algorithms for inner approximating the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Optimal designs are required to make efficient statistical experiments. D-optimal designs for some models are calculated by using canonical moments. On the other hand, integrable systems are dynamical systems whose solutions can be written…
Decision making algorithms are used in a multitude of different applications. Conventional approaches for designing decision algorithms employ principled and simplified modelling, based on which one can determine decisions via tractable…
Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from…
We investigate R-optimal designs for multi-response regression models with multi-factors, where the random errors in these models are correlated. Several theoretical results are derived for Roptimal designs, including scale invariance,…
We investigate the possibility of extending some results of Pazman and Pronzato (2014) to a larger set of optimality criteria. Namely, in a linear regression model the problem of computing D-, A-, E_k-optimal designs, of combining these…
This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…
In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…
A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In…