Related papers: S-SOS: Stochastic Sum-Of-Squares for Parametric Po…
This paper presents algorithms that upper-bound the peak value of a state function along trajectories of a continuous-time system with rational dynamics. The finite-dimensional but nonconvex peak estimation problem is cast as a convex…
Many previous Sum-of-Squares (SOS) lower bounds for CSPs had two deficiencies related to global constraints. First, they were not able to support a "cardinality constraint", as in, say, the Min-Bisection problem. Second, while the…
We study polynomial optimization problems whose objective has a composition or tensor train structure. These polynomials can be evaluated as a sequence of maps, giving rise to intermediate variables (``states'') of dimension lower than the…
It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using $(s\,d)^{O(n)}$ arithmetic operations, where $n$ and $s$ are the numbers of…
We compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gr\"obner bases, resultants, homotopy methods) are dramatically outperformed by a relaxation…
We present Ca$\Sigma$oS, the first MATLAB software specifically designed for nonlinear sum-of-squares optimization. A symbolic polynomial algebra system allows to formulate parametrized sum-of-squares optimization problems and facilitates…
In this paper, we address the effective degree bound problem for Lasserre's hierarchy of moment-sum-of-squares (SOS) relaxations in polynomial optimization involving $n$ variables. We assume that the first $n$ equality constraint…
Symmetric submodular maximization is an important class of combinatorial optimization problems, including MAX-CUT on graphs and hyper-graphs. The state-of-the-art algorithm for the problem over general constraints has an approximation ratio…
Selection of perefect parameters for low-pass filters can sometimes be an expensive problem with no analytical solution or differentiability of cost function. In this paper, we introduce a new PSO-inspired algorithm, that incorporates the…
Stochastic computer simulations enable users to gain new insights into complex physical systems. Optimization is a common problem in this context: users seek to find model inputs that maximize the expected value of an objective function.…
The Lasserre/Sum-of-Squares (SoS) hierarchy is a systematic procedure for constructing a sequence of increasingly tight semidefinite relaxations. It is known that the hierarchy converges to the 0/1 polytope in n levels and captures the…
We introduce an S.o.S hierarchy of lower bounds for a polynomial optimization problem whose constraint is expressed as a matrix polynomial semidefinite inequality. Our approach involves utilizing a penalty function framework to directly…
Let $P:\{0,1\}^k \to \{0,1\}$ be a nontrivial $k$-ary predicate. Consider a random instance of the constraint satisfaction problem $\mathrm{CSP}(P)$ on $n$ variables with $\Delta n$ constraints, each being $P$ applied to $k$ randomly chosen…
In this paper we study the problem of maximizing the distance to a given point over an intersection of balls. It was already known that this problem can be solved in polynomial time and space if the given point is not in the convex hull of…
We consider semidefinite programs (SDPs) of size n with equality constraints. In order to overcome scalability issues, Burer and Monteiro proposed a factorized approach based on optimizing over a matrix Y of size $n$ by $k$ such that $X =…
Load forecasting is a fundamental task in smart grid. Many techniques have been applied to developing load forecasting models. Due to the challenges such as the Curse of Dimensionality, overfitting, and limited computing resources,…
This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…
We consider the problem of finding the global optimum of a real-valued complex polynomial on a compact set defined by real-valued complex polynomial inequalities. It reduces to solving a sequence of complex semidefinite programming…
We propose a homogeneous primal-dual interior-point method to solve sum-of-squares optimization problems by combining non-symmetric conic optimization techniques and polynomial interpolation. The approach optimizes directly over the…
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…