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A rational number is dyadic if it has a finite binary representation $p/2^k$, where $p$ is an integer and $k$ is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in…
A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…
We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both…
We study a colourful generalization of the linear programming feasibility problem, comparing the algorithms introduced by Barany and Onn with new methods. We perform benchmarking on generic and ill-conditioned problems, as well as as…
Instances generation is crucial for linear programming algorithms, which is necessary either to find the optimal pivot rules by training learning method or to evaluate and verify corresponding algorithms. This study proposes a general…
We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
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…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its…
We consider the disjoint bilinear programming problem in which one of the disjoint subsets has the structure of an acute-angled polytope. An optimality criterion for such a problem is formulated and proved, and based on this, a polynomial…
We consider parametric linear programming problems with multiple objective functions depending linearly on some parameter. Both parametric (single-objective) linear programming and (non-parametric) multi-objective linear programming are…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
We empirically evaluate the finite-time performance of several simulation-optimization algorithms on a testbed of problems with the goal of motivating further development of algorithms with strong finite-time performance. We investigate if…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are…