Related papers: Unconstrained inverse quadratic programming proble…
Data-driven inverse optimization for mixed-integer linear programs (MILPs), which seeks to learn an objective function and constraints consistent with observed decisions, is important for building accurate mathematical models in a variety…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
Quadratic invariance is a condition which has been shown to allow for optimal decentralized control problems to be cast as convex optimization problems. The condition relates the constraints that the decentralization imposes on the…
Least squares form one of the most prominent classes of optimization problems, with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must…
In this paper we analyze and solve eigenvalue programs, which consist of the task of minimizing a function subject to constraints on the "eigenvalues" of the decision variable. Here, by making use of the FTvN systems framework introduced by…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
We consider least squares semidefinite programming (LSSDP) where the primal matrix variable must satisfy given linear equality and inequality constraints, and must also lie in the intersection of the cone of symmetric positive semidefinite…
For general quadratically-constrained quadratic programming (QCQP), we propose a parabolic relaxation described with convex quadratic constraints. An interesting property of the parabolic relaxation is that the original non-convex feasible…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…
A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…
Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…
Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…
A class of interior point methods using inexact directions is analysed. The linear system arising in interior point methods for linear programming is reformulated such that the solution is less sensitive to perturbations in the right-hand…
In this paper we consider a system of quadratic equations |<z_j, x>|^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be…
We propose a new polynomial-time algorithm for linear programming. We further extend the ideas used in this new linear programming algorithm for nonlinear programming problems. The new algorithm is based on the idea of treating the…
This article introduces a new physics-guided Machine Learning framework, with which we solve the generally non-invertible, ill-conditioned problems through an analytical approach and constrain the solution to the approximate inverse with…
This paper proposes QPALM, a proximal augmented Lagrangian method based on quadratic approximations, for solving nonlinear programming problems with weakly convex objective and constraint functions. The algorithm is constructed by…
The inverse potential problem consists in determining the density of the volume potential from measurements outside the sources. Its ill-posedness is due both to the non-uniqueness of the solution and to the instability of the solution with…