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
This paper conducts variational analysis of circular programs, which form a new class of optimization problems in nonsymmetric conic programming important for optimization theory and its applications. First we derive explicit formulas in terms of the initial problem data to calculate various generalized derivatives/coderivatives of the projection operator associated with the circular cone. Then we … Read more
The Internet is currently mostly exploited as a means to perform massive digital content distribution. Such a usage profile was not specifically taken into account while initially designing the architecture of the network: as a matter of fact, the Internet was instead conceived around the concept of host-to-host communications between two remote machines. To solve … Read more
This work addresses the issue of separating two finite sets in $\mathbb{R}^n $ by means of a suitable revolution cone $$ \Gamma (z,y,s)= \{x \in \mathbb{R}^n : s\,\Vert x-z\Vert – y^T(x-z)=0\}.$$ The specific challenge at hand is to determine the aperture coefficient $s$, the axis $y$, and the apex $z$ of the cone. These parameters … Read more