Related papers: Inverse polynomial optimization
Permutation polynomials (PPs) and their inverses have applications in cryptography, coding theory and combinatorial design theory. In this paper, we make a brief summary of the inverses of PPs of finite fields, and give the inverses of all…
Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a…
We are interested in the existence of Pareto solutions to the vector optimization problem $$\text{Min}_{\,\mathbb{R}^m_+} \{f(x) \,|\, x\in \mathbb{R}^n\},$$ where $f\colon\mathbb{R}^n\to \mathbb{R}^m$ is a polynomial map. By using the {\em…
These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…
We introduce a unified framework for computing approximately-optimal preconditioners for solving linear and non-linear systems of equations. We demonstrate that the condition number minimization problem, under structured transformations…
This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector $f \in \R^n$ from corrupted measurements $y = A f + e$. Here, $A$ is an $m$ by $n$ (coding)…
Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitous in quantum information theory and, more in general,…
We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion. The solution is approximated by a deep neural network which is the minimizer of a cost…
Many research has been conducted about quadratic programming and inverse optimization. In this paper we present the combination aspect of these subjects, applying on transportation problem. First, we obtain the inverse form of quadratic…
We consider the problem of minimizing a polynomial function over the integer lattice. Though impossible in general, we use a known sufficient condition for the existence of continuous minimizers to guarantee the existence of integer…
In this paper we design a new primal-dual algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint achieving the optimal approximation of $(1-1/e)$. This…
An algorithm $M$ is described that solves any well-defined problem $p$ as quickly as the fastest algorithm computing a solution to $p$, save for a factor of 5 and low-order additive terms. $M$ optimally distributes resources between the…
Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem to a constrained optimization problem…
We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on…
Numerical optimization for the inverse design of photonic structures is a tool which is providing increasingly convincing results -- even though the wave nature of problems in photonics makes them particularly complex. In the meantime, the…
We characterize approximate global optimal solutions (${\varepsilon}$-optima) to reverse optimization problems, namely, problems whose non-convex constraint is of the form $h(x) \geq 0$. This issue has not been addressed previously in the…
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…
We provide upper bounds on the total number of irreducible factors, and in particular irreducibility criteria for some classes of bivariate polynomials $f(x,y)$ over an arbitrary field $\mathbb{K}$. Our results rely on information on the…
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…
Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that…