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We develop a practical semidefinite programming (SDP) facial reduction procedure that utilizes computationally efficient approximations of the positive semidefinite cone. The proposed method simplifies SDPs with no strictly feasible…
Maximizing a non-negative, monontone, submodular function $f$ over $n$ elements under a cardinality constraint $k$ (SMCC) is a well-studied NP-hard problem. It has important applications in, e.g., machine learning and influence…
Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…
We point out that Chubanov's oracle-based algorithm for linear programming [5] can be applied almost as it is to linear semi-infinite programming (LSIP). In this note, we describe the details and prove the polynomial complexity of the…
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 =…
Memory is a key computational bottleneck when solving large-scale convex optimization problems such as semidefinite programs (SDPs). In this paper, we focus on the regime in which storing an $n\times n$ matrix decision variable is…
We introduce fast randomized algorithms for solving semidefinite programming (SDP) relaxations of the partial permutation synchronization (PPS) problem, a core task in multi-image matching with significant relevance to 3D reconstruction.…
We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement…
It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load…
Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
In light of the increased focus on distributed methods, this paper proposes two accelerated subgradient methods and an adaptive penalty parameter scheme to speed-up the convergence of ADMM on the component-based dual decomposition of the…
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal…
We consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs). We establish a probabilistic bridge from the…
A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear…
A simple characterization of the solvability of power flow equations is of great importance in the monitoring, control, and protection of power systems. In this paper, we introduce a sufficient condition for power flow Jacobian…
This paper considers coordinated multicast beamforming in a multi-cell wireless network. Each multiantenna base station (BS) serves multiple groups of single antenna users by generating a single beam with common data per group. The aim is…
Motivated by the expressive power of completely positive programming to encode hard optimization problems, many approximation schemes for the completely positive cone have been proposed and successfully used. Most schemes are based on outer…
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…
A robust adaptive model predictive control (MPC) algorithm is presented for linear, time invariant systems with unknown dynamics and subject to bounded measurement noise. The system is characterized by an impulse response model, which is…