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An optimization problem considering AC power flow constraints and integer decision variables can usually be posed as a mixed-integer quadratically constrained quadratic program (MIQCQP) problem. In this paper, first, a set of valid linear…
Semidefinite programming (SDP) is a unifying framework that generalizes both linear programming and quadratically-constrained quadratic programming, while also yielding efficient solvers, both in theory and in practice. However, there exist…
In 2020, Yamakawa and Okuno proposed a stabilized sequential quadratic semidefinite programming (SQSDP) method for solving, in particular, degenerate nonlinear semidefinite optimization problems. The algorithm is shown to converge globally…
A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink…
This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization…
Integer semidefinite programming (ISDP) has recently gained attention due to its connection to binary quadratically constrained quadratic programs (BQCQPs), which can be exactly reformulated as binary semidefinite programs (BSDPs). However,…
We develop a general framework for finding approximately-optimal preconditioners for solving linear systems. Leveraging this framework we obtain improved runtimes for fundamental preconditioning and linear system solving problems including…
Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…
We propose an estimation method for quantum measurement tomography (QMT) based on semidefinite programming (SDP), and discuss how it may be employed to detect experimental imperfections, such as shot noise and/or faulty preparation of the…
In the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual or the NT direction,…
We present a new generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite…
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture,…
Approximate message passing (AMP) is a family of iterative algorithms that generalize matrix power iteration. AMP algorithms are known to optimally solve many average-case optimization problems. In this paper, we show that a large class of…
Symmetric extensions are essential in quantum mechanics, providing a lens to investigate the correlations of entangled quantum systems and to address challenges like the quantum marginal problem. Though semi-definite programming (SDP) is a…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
Although neural networks have been applied to several systems in recent years, they still cannot be used in safety-critical systems due to the lack of efficient techniques to certify their robustness. A number of techniques based on convex…
In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common…
Low-rank methods for semidefinite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are hard to implement…
Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…
We study a semidefinite programming (SDP) relaxation of the maximum likelihood estimation for exactly recovering a hidden community of cardinality $K$ from an $n \times n$ symmetric data matrix $A$, where for distinct indices $i,j$, $A_{ij}…