Related papers: A "joint+marginal" algorithm for polynomial optimi…
This paper is concerned with polynomial optimization problems. We show how to exploit term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of semidefinite programming relaxations. The novelty (and…
This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…
We consider the NP-hard problem of minimizing a separable concave quadratic function over the integral points in a polyhedron, and we denote by D the largest absolute value of the subdeterminants of the constraint matrix. In this paper we…
We consider the problem of planning with participation constraints introduced in [Zhang et al., 2022]. In this problem, a principal chooses actions in a Markov decision process, resulting in separate utilities for the principal and the…
The problem of optimizing over the cone of nonnegative polynomials is a fundamental problem in computational mathematics, with applications to polynomial optimization, control, machine learning, game theory, and combinatorics, among others.…
It was recently shown [7, 9] that "properly built" linear and polyhedral estimates nearly attain minimax accuracy bounds in the problem of recovery of unknown signal from noisy observations of linear images of the signal when the signal set…
We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem $\min_{\mathbf{x} \in \mathbf{S}}\{ (f_1(\mathbf{x}), f_2(\mathbf{x})) \}$, where $f_1$ and $f_2$ are two…
We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
We study the problem of minimizing a multivariate polynomial function over the unit hypercube. By representing the polynomial through a hypergraph and exploiting its sparsity structure, we establish a new sufficient condition under which…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…
In this paper, we focus on computing local minimizers of a multivariate polynomial optimization problem under certain genericity conditions. By using a technique in computer algebra and the second-order optimality condition, we provide a…
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian…
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice ${\bf Z}^n$. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the…
Quaternion optimization has attracted significant interest due to its broad applications, including color face recognition, video compression, and signal processing. Despite the growing literature on quadratic and matrix quaternion…
Let the objective unction \( f \) depends on the target variable \( x \) along with a nuisance variable \( s \): \( f(v) = f(x,s) \). The goal is to identify the marginal solution \( x^{*} = \arg\min_{x} \min_{s} f(x,s) \). This paper…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial function with parameters subject to semialgebraic constraints.…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…