Related papers: Speeding Up Logico-Numerical Strategy Iteration (e…
Polyhedral projection is a main operation of the polyhedron abstract domain.It can be computed via parametric linear programming (PLP), which is more efficient than the classic Fourier-Motzkin elimination method.In prior work, PLP was done…
Acceleration of algorithms is becoming a crucial problem, if larger data sets are to be processed. Evaluation of algorithms is mostly done by using computational geometry approach and evaluation of computational complexity. However in…
In this paper we discuss $\l$-policy iteration, a method for exact and approximate dynamic programming. It is intermediate between the classical value iteration (VI) and policy iteration (PI) methods, and it is closely related to optimistic…
We present a technique for automatically extracting mutual exclusion invariants from temporal planning instances. It first identifies a set of invariant templates by inspecting the lifted representation of the domain and then checks these…
Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…
Linear programming (LP) is an extremely useful tool and 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…
The solution of a (stochastic) differential equation can be locally approximated by a (stochastic) expansion. If the vector field of the differential equation is a polynomial, the corresponding expansion is a linear combination of iterated…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…
We study reinforcement learning (RL) with transition look-ahead, where the agent may observe which states would be visited upon playing any sequence of $\ell$ actions before deciding its course of action. While such predictive information…
This paper proposes an optimization-based task and motion planning framework, named "Logic Network Flow", that integrates temporal logic specifications into mixed-integer programs for efficient robot planning. Inspired by the…
Programs admitting a polyhedral representation can be transformed in many ways for locality and parallelism, notably loop tiling. Data flow analysis can then compute dependence relations between iterations and between tiles. When tiling is…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a…
Automatic verification of concurrent programs faces state explosion due to the exponential possible interleavings of its sequential components coupled with large or infinite state spaces. An alternative is deductive verification, where…
The increasing digitalization in industry and society leads to a growing abundance of data available to be processed and exploited. However, the high volume of data requires considerable computational resources for applying machine learning…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
In this paper we propose a novel methodology for static analysis of binary code using abstract interpretation. We use an abstract domain based on polyhedra and two mapping functions that associate polyhedra variables with registers and…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…