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A new algorithm for solving the solution of the linear-quadratic optimization problem (LQP) with unseparated boundary conditions in the continuous case is given. Using the properties of symmetry of the corresponding Hamiltonian matrix, the…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…
A novel approach to exploiting the log-convex structure present in many design problems is developed by modifying the classical Sequential Quadratic Programming (SQP) algorithm. The modified algorithm, Logspace Sequential Quadratic…
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…
We study approximation algorithms for scheduling problems with the objective of minimizing total weighted completion time, under identical and related machine models with job precedence constraints. We give algorithms that improve upon many…
Currently, the simplex method and the interior point method are indisputably the most popular algorithms for solving linear programs, LPs. Unlike general conic programs, LPs with a finite optimal value do not require strict feasibility in…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. It is proved that the basis of the ideal of…
Unlike in TFNP, for which there is an abundance of problems capturing natural existence principles which are incomparable (in the black-box setting), Kleinberg et al. [KKMP21] observed that many of the natural problems considered so far in…
For a given rational number $x$ and an integer $s\geq 1$, let us consider a generalized polylogarithmic function, often called the Lerch function, defined by $$\Phi_{s}(x,z)= \sum_{k=0}^{\infty}\frac{z^{k+1}}{(k+x+1)^s}\enspace.$$ We prove…
We study the lift-and-project relaxations of the stable set polytope of graphs generated by $\text{LS}_+$, the SDP lift-and-project operator devised by Lov\'{a}sz and Schrijver. Our focus is on $\ell$-minimal graphs: graphs on $3\ell$…
Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…
Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that…
In the last few years, the notion of symmetry has provided a powerful and essential lens to view several optimization or sampling problems that arise in areas such as theoretical computer science, statistics, machine learning, quantum…
Symmetry in integer programming causes redundant search and is often handled with symmetry breaking constraints that remove as many equivalent solutions as possible. We propose an algebraic method which allows to generate a random family of…
A polynomial-time algorithm for 0-1 integer linear programmings has been proposed. This method continues the classic idea of solving ILP with its LP relaxation. The innovation is that every constraint in the LP is reconstructed into a…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…
Metric facility location is a well-studied problem for which linear programming methods have been used with great success in deriving approximation algorithms. The capacity-constrained generalizations, such as capacitated facility location…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…