Abstract—In this article, we introduce new techniques to solve the nonlinear regression problem and the nonlinear classification problem. Our benchmarks suggest that our method for regression is significantly more effective when compared to classical methods and our method for classification is competitive. Our list of classical methods includes least squares, random forests, decision trees, boosted … Read more
Assume we are given a system of ordinary differential equations x 0 = f(x, p) depending on a parameter p ∈ R pe . In this dissertation we consider the problem of locating a parameter p and an initial condition ξ that give rise to a heteroclinic orbit. In the case that such p and … Read more
This paper proposes a method for eliminating multicollinearity from linear regression models. Specifically, we select the best subset of explanatory variables subject to the upper bound on the condition number of the correlation matrix of selected variables. We first develop a cutting plane algorithm that, to approximate the condition number constraint, iteratively appends valid inequalities … Read more
TMAC is a toolbox written in C++11 that implements algorithms based on a set of mod- ern methods for large-scale optimization. It covers a variety of optimization problems, which can be both smooth and nonsmooth, convex and nonconvex, as well as constrained and unconstrained. The algorithms implemented in TMAC, such as the coordinate up- date … Read more
To receive a project contract through competitive bidding, contractors submit a bid price determined by putting a markup on the estimated project cost. Since a bid is inevitably affected by an inaccurate cost estimate, sufficient resources should be allocated to cost estimation. This paper develops a novel optimization model for determining the bid markup and … Read more
Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct computation is too intensive, and they have thus to be estimated online from the observed signals. For batch optimization of … Read more
We consider the problem of computing optimal traffic light programs for urban road intersections using traffic flow conservation laws on networks. Based on a Partial Outer Convexification approach, which has been successfully applied in the area of mixed-integer optimal control for systems of ordinary or differential algebraic equations, we develop a computationally tractable two-stage solution … Read more
This paper presents a reformulation that is a natural “by-product” of the ‘variable endogenization’ process for equality-constrained programs. The method results a partial relaxation of the constraints which in turn confers some computational advantages. A fully-annotated example illustrates the technique and presents some comparative numerical results. CitationSiwale, I.: Partial Relaxation of Equality-constrained Programs. Technical Report … Read more
The study of matrix inequalities in a dimension-free setting is in the realm of free real algebraic geometry (RAG). In this paper we investigate constrained trace and eigenvalue optimization of noncommutative polynomials. We present Lasserre’s relaxation scheme for trace optimization based on semidefinite programming (SDP) and demonstrate its convergence properties. Finite convergence of this relaxation … Read more
We introduce a family of subadditive functions called Generator Functions for mixed integer linear programs. These functions were previously defined for pure integer programs with non-negative entries by Klabjan [13]. They are feasible in the subadditive dual and we show that they are enough to achieve strong duality. Several properties of the functions are shown. … Read more