Related papers: SOSOPT: A Toolbox for Polynomial Optimization
Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…
This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one…
This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many…
We introduce PoCET: a free and open-scource Polynomial Chaos Expansion Toolbox for Matlab, featuring the automatic generation of polynomial chaos expansion (PCE) for linear and nonlinear dynamic systems with time-invariant stochastic…
We propose SonOpt, the first (open source) data sonification application for monitoring the progress of bi-objective population-based optimization algorithms during search, to facilitate algorithm understanding. SonOpt provides insights…
SPSMAT (Spectral/Pseudospectral matrix method) is an add-on for Octave, that helps you solve nonfractional-/fractional ordinary/partial differential/integral equations. In this version, as the first version, the well-defined spectral or…
This paper studies robust solutions and semidefinite linear programming (SDP) relaxations of a class of convex polynomial programs in the face of data uncertainty. The class of convex programs, called robust SOS-convex programs, includes…
When sum-of-squares (SOS) programs are recast as semidefinite programs (SDPs) using the standard monomial basis, the constraint matrices in the SDP possess a structural property that we call \emph{partial orthogonality}. In this paper, we…
This paper studies the copositive optimization problem whose objective is a sparse polynomial, with linear constraints over the nonnegative orthant. We propose sparse Moment-SOS relaxations to solve it. Necessary and sufficient conditions…
We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the…
In this paper we discuss the theory used in the design of an open source lightmorphic signatures analysis toolkit (LSAT). In addition to providing a core functionality, the software package enables specific optimizations with its modular…
Software engineers must make decisions that trade off competing goals (faster vs. cheaper, secure vs. usable, accurate vs. interpretable, etc.). Despite MSR's proven techniques for exploring such goals, researchers still struggle with these…
This paper focuses on the study of a mathematical program with equilibrium constraints, where the objective and the constraint functions are all polynomials. We present a method for finding its global minimizers and global minimum using a…
This paper presents exact Semi-Definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-convex functions and projected spectrahedral support sets.…
In this paper, we present a toolbox for structured model reduction developed for MATLAB. In addition to structured model reduction methods using balanced realizations of the subsystems, we introduce a numerical algorithm for structured…
This paper introduces zonoLAB, a MATLAB-based toolbox for set-based control system analysis using the hybrid zonotope set representation. Hybrid zonotopes have proven to be an expressive set representation that can exactly represent the…
This work introduces StageSAT, a new approach to solving floating-point satisfiability that bridges SMT solving with numerical optimization. StageSAT reframes a floating-point formula as a series of optimization problems in three stages of…
The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in…
The goal of this paper is to present an overview of the software collection for the solution of linear and nonlinear semidefinite optimization problems PENNON. In the first part we present theoretical and practical details of the underlying…
In this paper, we present a toolbox for a specific optimization problem that frequently arises in bioinformatics or genomics. In this specific optimisation problem, the state space is a set of words of specified length over a finite…