Related papers: Term-sparse polynomial optimization for the design…

Nonnegative least squares problems with multiple right-hand sides (MNNLS) arise in models that rely on additive linear combinations. In particular, they are at the core of most nonnegative matrix factorization algorithms and have many…

We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of $\ell_\infty$-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when…

An approach to obtaining a parsimonious polynomial model from time series is proposed. An optimal minimal nonuniform time series embedding schema is used to obtain a time delay kernel. This scheme recursively optimizes an objective…

A multiobjective optimization method is proposed for obtaining the optimal plane trusses simultaneously for various aspect ratios of the initial ground structure as a set of Pareto optimal solutions generated through a single optimization…

Sum of squares (SOS) optimization is a powerful technique for solving problems where the positivity of a polynomials must be enforced. The common approach to solve an SOS problem is by relaxation to a Semidefinite Program (SDP). The main…

We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy. Our…

The area of topology optimization of continuum structures of which is allowed to change in order to improve the performance is now dominated by methods that employ the material distribution concept. The typical methods of the topology…

We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…

We study planted problems---finding hidden structures in random noisy inputs---through the lens of the sum-of-squares semidefinite programming hierarchy (SoS). This family of powerful semidefinite programs has recently yielded many new…

A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…

Autonomous navigation requires an accurate model or map of the environment. While dramatic progress in the prior two decades has enabled large-scale SLAM, the majority of existing methods rely on non-linear optimization techniques to find…

Topology optimization (TO) in two dimensions often presents a trade-off between structural performance and manufacturability, with unpenalized (variable-thickness) methods yielding superior but complex designs, and penalized (SIMP) methods…

This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…

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)…

This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if the objective can be written as a sum of sparse nonnegative…

Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…

In this paper we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specifications. Our approach utilizes multi-material microstructures as low-level building blocks…

In this article, we provide a new algorithm for solving constraint satisfaction problems over templates with few subpowers, by reducing the problem to the combination of solvability of a polynomial number of systems of linear equations over…

This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove…

AC-OPF (Alternative Current Optimal Power Flow)aims at minimizing the operating costs of a power gridunder physical constraints on voltages and power injections.Its mathematical formulation results in a nonconvex polynomial…