Related papers: Semidefinite relaxations in optimal experiment des…
The Quadratic Assignment Problem (QAP) is an important discrete optimization instance that encompasses many well-known combinatorial optimization problems, and has applications in a wide range of areas such as logistics and computer vision.…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators,…
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…
We study how to solve semidefinite programming relaxations for large scale polynomial optimization. When interior-point methods are used, typically only small or moderately large problems could be solved. This paper studies regularization…
This two-part paper is concerned with the problem of minimizing a linear objective function subject to a bilinear matrix inequality (BMI) constraint. In this part, we first consider a family of convex relaxations which transform BMI…
In this paper, by improving the variable-splitting approach, we propose a new semidefinite programming (SDP) relaxation for the nonconvex quadratic optimization problem over the $\ell_1$ unit ball (QPL1). It dominates the state-of-the-art…
We introduce a generic technique to obtain linear relaxations of semidefinite programs with provable guarantees based on the commutativity of the constraint and the objective matrices. We study conditions under which the optimal value of…
We consider the problem of inference in higher-order undirected graphical models with binary labels. We formulate this problem as a binary polynomial optimization problem and propose several linear programming relaxations for it. We compare…
We consider the strictly correlated electron (SCE) limit of the fermionic quantum many-body problem in the second-quantized formalism. This limit gives rise to a multi-marginal optimal transport (MMOT) problem. Here the marginal state space…
In this paper, we propose a multi-input multi-output beamforming transmit optimization model for joint radar sensing and multi-user communications, where the design of the beamformers is formulated as an optimization problem whose objective…
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…
We study the convex relaxation of a polynomial optimization problem, maximizing a product of linear forms over the complex sphere. We show that this convex program is also a relaxation of the permanent of Hermitian positive semidefinite…
We develop a new approach to robust adaptive beamforming in the presence of signal steering vector errors. Since the signal steering vector is known imprecisely, its presumed (prior) value is used to find a more accurate estimate of the…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
Semidefinite relaxation techniques have shown great promise for nonconvex optimal power flow problems. However, a number of independent numerical experiments have led to concerns about scalability and robustness of existing SDP solvers. To…
A relaxation method based on border basis reduction which improves the efficiency of Lasserre's approach is proposed to compute the optimum of a polynomial function on a basic closed semi algebraic set. A new stopping criterion is given to…
Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phe-nomena, by relaxing controls as Young measures. These semi-definite…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
This paper proposes a general fixture layout design framework that directly integrates the system equation with the convex relaxation method. Note that the optimal fixture design problem is a large-scale combinatorial optimization problem,…