Related papers: Solving cluster moment relaxation with hierarchica…
This paper studies how to compute global minimizers of the cubic-quartic regularization (CQR) problem \[ \min_{s \in \mathbb{R}^n} \quad f_0+g^Ts+\frac{1}{2}s^THs+\frac{\beta}{6} \| s \|^3+\frac{\sigma}{4} \| s \|^4, \] where $f_0$ is a…
We consider the problem of optimal input design for estimating uncertain parameters in a discrete-time linear state space model, subject to simultaneous amplitude and l1/l2-norm constraints on the admissible inputs. We formulate this…
This paper proposes a new framework for the optimization of excitation inputs for system identification. The optimization problem considered is to maximize a reduced Fisher information matrix in any of the classical D-, E-, or A-optimal…
This work deals with the efficient numerical solution of the time-fractional heat equation discretized on non-uniform temporal meshes. Non-uniform grids are essential to capture the singularities of "typical" solutions of time-fractional…
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…
Lasserre's moment-SOS hierarchy consists of approximating instances of the generalized moment problem (GMP) with moment relaxations and sums-of-squares (SOS) strenghtenings that boil down to convex semidefinite programming (SDP) problems.…
The Standard Quadratic optimization Problem (StQP), arguably the simplest among all classes of NP-hard optimization problems, consists of extremizing a quadratic form (the simplest nonlinear polynomial) over the standard simplex (the…
This paper introduces several new algorithms for consensus over the special orthogonal group. By relying on a convex relaxation of the space of rotation matrices, consensus over rotation elements is reduced to solving a convex problem with…
We study quantum algorithms for approximating Lasserre's hierarchy values for polynomial optimization. Let $f,g_1,\ldots,g_m$ be real polynomials in $n$ variables and $f^\star$ the infimum of $f$ over the semialgebraic set $S(g)=\{x:…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
Visualizing graphs using virtual physical models is probably the most heavily used technique for drawing graphs in practice. There are many algorithms that are efficient and produce high-quality layouts. If one requires that the layout also…
We explore some connections between association schemes and the analyses of the semidefinite programming (SDP) based convex relaxations of combinatorial optimization problems in the Lov\'{a}sz--Schrijver lift-and-project hierarchy. Our…
In this paper, we propose an iterative algorithm to address the nonconvex multi-group multicast beamforming problem with quality-of-service constraints and per-antenna power constraints. We formulate a convex relaxation of the problem as a…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
This paper proposes a bilevel hierarchy of strengthened complex moment relaxations for complex polynomial optimization. The key trick entails considering a class of positive semidefinite conditions that arise naturally in characterizing the…
This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable…
The "exact subgraph" approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
For a large class of optimization problems, namely those that can be expressed as finite-valued constraint satisfaction problems (VCSPs), we establish a dichotomy on the number of levels of the Lasserre hierarchy of semi-definite programs…
For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…
Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…