Related papers: Invariant semidefinite programs
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
We propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve SDPs work in the space of positive semidefinite matrices. Contrary to that the proposed…
Motivated by applications in wireless communications, this paper develops semidefinite programming (SDP) relaxation techniques for some mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation…
Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…
In the last decade, decision diagrams (DDs) have been the basis for a large array of novel approaches for modeling and solving optimization problems. Many techniques now use DDs as a key tool to achieve state-of-the-art performance within…
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.…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present…
Semidefinite programs (SDPs) are powerful theoretical tools that have been studied for over two decades, but their practical use remains limited due to computational difficulties in solving large-scale, realistic-sized problems. In this…
Achieving safe control under uncertainty is a key problem that needs to be tackled for enabling real-world autonomous robots and cyber-physical systems. This paper introduces Probabilistic Safety Programs (PSP) that embed both the…
In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite…
A longstanding problem related to floating-point implementation of numerical programs is to provide efficient yet precise analysis of output errors. We present a framework to compute lower bounds on largest absolute roundoff errors, for a…
Numerical semigroups have been extensively studied throughout the literature, and many of their invariants have been characterized. In this work, we generalize some of the most important results about symmetry, pseudo-symmetry, or…
Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly…
Finite Turing computation has a fundamental symmetry between inputs, outputs, programs, time, and storage space. Standard models of transfinite computational break this symmetry; we consider ways to recover it and study the resulting model…
These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…
Delsarte's method and its extensions allow to consider the upper bound problem for codes in 2-point-homogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that…
This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properties of the matrix-valued mapping defined upon the Huber…
We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility and optimality using the framework of formally real Jordan…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…