Related papers: Efficiently expressing feasibility problems in Lin…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
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…
We introduce an extension of decision problems called resiliency problems. In resiliency problems, the goal is to decide whether an instance remains positive after any (appropriately defined) perturbation has been applied to it. To tackle…
We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called $2$-stage stochastic. A $2$-stage stochastic ILP is an integer program of the form $\min…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
In this paper we introduce a class of constraint logic programs such that their termination can be proved by using affine level mappings. We show that membership to this class is decidable in polynomial time.
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of…
We approximate the backward reachable set of discrete-time autonomous polynomial systems using the recently developed occupation measure approach. We formulate the problem as an infinite-dimensional linear programming (LP) problem on…
We study the general integer programming (IP) problem of optimizing a separable convex function over the integer points of a polytope: $\min \{f(\mathbf{x}) \mid A\mathbf{x} = \mathbf{b}, \, \mathbf{l} \leq \mathbf{x} \leq \mathbf{u}, \,…
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…
We address lower bounds on the time complexity of algorithms solving the propositional satisfiability problem. Namely, we consider two DPLL-type algorithms, enhanced with the unit clause and pure literal heuristics. Exponential lower bounds…
We analyse the asymptotic properties of a continuous-time, two-timescale stochastic approximation algorithm designed for stochastic bilevel optimisation problems in continuous-time models. We obtain the weak convergence rate of this…
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…
Recent work on approximate linear programming (ALP) techniques for first-order Markov Decision Processes (FOMDPs) represents the value function linearly w.r.t. a set of first-order basis functions and uses linear programming techniques to…
We propose a framework for sensitivity analysis of linear programs (LPs) in minimization form, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact,…
This paper investigates several cost-sparsity induced optimal input selection problems for structured systems. Given are an autonomous system and a prescribed set of input links, where each input link has a non-negative cost. The problems…
In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
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…