Related papers: Optimization over trace polynomials
Let H be a positive semidefinite matrix partitioned into Hermitian blocks. Then, up to a direct sum operation, H is the average of matrices isometrically congruent to its partial trace. A few corollaries are given, related to important…
This paper studies the problem of maximizing the sum of traces of matrix quadratic forms on a product of Stiefel manifolds. This orthogonal trace-sum maximization (OTSM) problem generalizes many interesting problems such as generalized…
A univariate trace polynomial is a polynomial in a variable x and formal trace symbols Tr(x^j). Such an expression can be naturally evaluated on matrices, where the trace symbols are evaluated as normalized traces. This paper addresses…
We develop randomized matrix-free algorithms for estimating partial traces, a generalization of the trace arising in quantum physics and chemistry. Our algorithm improves on the typicality-based approach used in [T. Chen and Y-C. Cheng,…
In this paper we study bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. We construct a hierarchy of semidefinite programming lower bounds on the minimal entanglement dimension of a…
Single-shot quantum information theory is governed not only by entropy exponents, but also by the finite-resource constants that multiply them. These constants directly affect the quantitative performance of decoupling, covering,…
In the past decades, one of the most fruitful approaches to the study of algebraic $K$-theory has been trace methods, which construct and study trace maps from algebraic $K$-theory to topological Hochschild homology and related invariants.…
Partial trace is a very important mathematical operation in quantum mechanics. It is not only helpful in studying the subsystems of a composite quantum system but also used in computing a vast majority of quantum entanglement measures.…
Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitous in quantum information theory and, more in general,…
Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today's leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant…
An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In…
This work explores an extension of machine learning-optimized piecewise polynomial approximation by incorporating energy optimization as an additional objective. Traditional closed-form solutions enable continuity and approximation targets…
Optimization over trained machine learning models has applications including: verification, minimizing neural acquisition functions, and integrating a trained surrogate into a larger decision-making problem. This paper formulates and solves…
In this paper, we study the polynomial optimization problem of multi-forms over the intersection of the multi-spheres and the nonnegative orthants. This class of problems is NP-hard in general, and includes the problem of finding the best…
In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…
By applying the new supersymmetric localization principle introduced in \cite{Choi:2021yuz,Choi:2023pjn}, we present two complementary approaches for the path integral derivation of the `non-chiral' trace formula for a semisimple compact…
In this paper, we propose an extension of trace ratio based Manifold learning methods to deal with multidimensional data sets. Based on recent progress on the tensor-tensor product, we present a generalization of the trace ratio criterion…
We investigate the extremal values of partial traces of matrix tensors under operator norm constraints. To evaluate these multi-linear quantities, we develop a comprehensive graphical formalism that encodes multi-leg partial traces, partial…
We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…
Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance…