相关论文: On the numerical solution of Lasserre relaxations …

This paper proposes an arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc…

Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…

In this paper, we propose novel algorithms for inferring the Maximum a Posteriori (MAP) solution of discrete pairwise random field models under multiple constraints. We show how this constrained discrete optimization problem can be…

In this paper, we proposed an interior point method for constrained optimization, which is characterized by the using of quasi-tangential subproblem. This algorithm follows the main ideas of primal dual interior point methods and…

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…

We study a primal-dual interior point method specialized to clustered low-rank semidefinite programs requiring high precision numerics, which arise from certain multivariate polynomial (matrix) programs through sums-of-squares…

This work is concerned with the numerical solution of large-scale symmetric positive definite matrix equations of the form $A_1XB_1^\top + A_2XB_2^\top + \dots + A_\ell X B_\ell^\top = F$, as they arise from discretized partial differential…

We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…

We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…

This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many…

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,…

Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…

We propose a novel preconditioned inexact primal-dual interior point method for constrained convex quadratic programming problems. The algorithm we describe invokes the preconditioned conjugate gradient method on a new reduced Schur…

Non-commutative polynomial optimization is a powerful technique with numerous applications in quantum nonlocality, quantum key distribution, causal inference, many-body physics, amongst others. The standard approach is to reduce such…

In this paper, we describe a new method to compute the minimum of a real polynomial function and the ideal defining the points which minimize this polynomial function, assuming that the minimizer ideal is zero-dimensional. Our method is a…

This paper proposes tight semidefinite relaxations for polynomial optimization. The optimality conditions are investigated. We show that generally Lagrange multipliers can be expressed as polynomial functions in decision variables over the…

We provide an interior point method based on quasi-Newton iterations, which only requires first-order access to a strongly self-concordant barrier function. To achieve this, we extend the techniques of Dunagan-Harvey [STOC '07] to maintain…

PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting $\rm L^1$ term within the objective…

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…