相关论文: Convex Hull Formulations for Mixed-Integer Multili…

Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…

A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…

In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding…

We study the convex hull of the graph of a quadratic function $f(\mathbf{x})=\sum_{ij\in E}x_ix_j$, where the sum is over the edge set of a graph $G$ with vertex set $\{1,\dots,n\}$. Using an approach proposed by Gupte et al. (Discrete…

A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…

This paper reviews some recent applications of the theory of the compensated convex transforms or of the proximity hull as developed by the authors to image processing and shape interrogation with special attention given to the Hausdorff…

We propose an approach based on convex relaxations for certifiably optimal robust multiview triangulation. To this end, we extend existing relaxation approaches to non-robust multiview triangulation by incorporating a truncated least…

Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…

We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. These inequalities can be utilized for solving numerous practical nonlinear discrete optimization problems from value-at-risk minimization to queueing…

Integral representations play a prominent role in the analysis of entire functions. The representations of generalized Mittag-Leffler type functions and their asymptotics have been (and still are) investigated by plenty of authors in…

The description of all solutions to the relaxed commutant lifting problem in terms of an underlying contraction, obtained earlier in joint work of the author with A.E. Frazho and M.A. Kaashoek, is transformed into a linear fractional…

Computing mixed volume of convex polytopes is an important problem in computational algebraic geometry. This paper establishes sufficient conditions under which the mixed volume of several convex polytopes exactly equals the normalized…

When using the standard McCormick inequalities twice to convexify trilinear monomials, as is often the practice in modeling and software, there is a choice of which variables to group first. For the important case in which the domain is a…

This paper is a survey on major results on Hilbert functions of multigraded algebras and mixed multiplicities of ideals, including their applications to the computation of Milnor numbers of complex analytic hypersurfaces with isolated…

Chance-constrained programming is a widely used framework for decision-making under uncertainty, yet its mixed-integer reformulations involve nonconvex mixing sets with a knapsack constraint, leading to weak relaxations and computational…

Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems,…

Mixed integer bilinear programs (MIBLPs) offer tools to resolve robotics motion planning problems with orthogonal rotation matrices or static moment balance, but require long solving times. Recent work utilizing data-driven methods has…

Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a…

We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…

This article gives necessary and sufficient conditions for the dual representation of Rockafellar in (Integrals which are convex functionals. II, Pacific J. Math., 39:439--469, 1971) for integral functionals on the space of continuous…