Related papers: A Unified Tool for Solving Uni-Parametric Linear P…
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport…
In this paper we develop a very special substitution method for solving a general linear programming problem (LPP). Of course the substitution is a kind of elimination of variable but this method must not be confused with the so-called…
We give a specific method to solve with quadratic complexity the linear systems arising in known algorithms to deal with the sign determination problem. In particular, this enable us to improve the complexity bound for sign determination in…
We present a new method for solving parametrized linear systems. Under certain assumptions on the parametrization, solutions to the linear systems for all parameters can be accurately approximated by linear combinations of solutions to…
We propose a combinatorial method for computing explicit solutions to multi-parametric quadratic programs, which can be used to compute explicit control laws for linear model predictive control. In contrast to classical methods, which are…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
In this paper, we consider the quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces. By using the Legendre property of quadratic forms or the compactness of operators in the presentations of…
In this paper, we provide an elementary, geometric, and unified framework to analyze conic programs that we call the strict complementarity approach. This framework allows us to establish error bounds and quantify the sensitivity of the…
We extend our two-scale neural-network method for scalar singularly perturbed problems with one small parameter to dynamical systems with multiple small parameters. To accommodate multiple small parameters, we use a single effective scale…
This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be…
Multi-objective verification problems of parametric Markov decision processes under optimality criteria can be naturally expressed as nonlinear programs. We observe that many of these computationally demanding problems belong to the…
In this paper we extend test set based augmentation methods for integer linear programs to programs with more general convex objective functions. We show existence and computability of finite test sets for these wider problem classes by…
In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the…
We consider discrete linear Chebyshev approximation problems in which the unknown parameters of linear function are fitted by minimizing the maximum absolute deviation of errors. Such problems find application in the solution of…
We study relaxations for linear programs with complementarity constraints, especially instances whose complementary pairs of variables are not independent. Our formulation is based on identifying vertex covers of the conflict graph of the…
A typical workflow for solving a linear programming problem is to first write a linear program parametrized by the data in a language such as Math GNU Prog or AMPL then call the solver on this program while providing the data. When the data…
This paper studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parametrization, the problem of finding the…
In the Integer Quadratic Programming problem input is an n*n integer matrix Q, an m*n integer matrix A and an m-dimensional integer vector b. The task is to find a vector x in Z^n, minimizing x^TQx, subject to Ax <= b. We give a fixed…
We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number…