Related papers: Solving MIPs via Scaling-based Augmentation
Mixed Integer Linear Programs (MILP) are well known to be NP-hard (Non-deterministic Polynomial-time hard) problems in general. Even though pure optimization-based methods, such as constraint generation, are guaranteed to provide an optimal…
Generalizing the simplex method, circuit augmentation schemes for linear programs follow circuit directions through the interior of the underlying polyhedron. Steepest-descent augmentation is especially promising, but an implementation of…
Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the…
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in…
Probing is an important presolving technique in mixed-integer programming solvers. It selects binary variables, tentatively fixes them to 0 and 1, and performs propagation to deduce additional variable fixings, bound tightenings,…
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…
Mixed-integer linear programming (MILP) plays a crucial role in artificial intelligence, biochemistry, finance, cryptography, etc. Notwithstanding popular for decades, the researches of MILP solvers are still limited by the resource…
Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which being the solver for the least squares problem $\min_{x}\lVert b-Ax\rVert_{2}$. By transforming least…
Mixed-integer linear programming (MILP) is at the core of many advanced algorithms for solving fundamental problems in combinatorial optimization. The complexity of solving MILPs directly correlates with their support size, which is the…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
Accurate structural relaxation is critical for advanced materials design. Traditional approaches built on physics-derived first-principles calculations are computationally expensive, motivating the creation of machine-learning interatomic…
We present new pivot rules for the Simplex method for LPs over 0/1 polytopes. We show that the number of non-degenerate steps taken using these rules is strongly polynomial and even linear in the dimension or in the number of variables. Our…
A standard approach to solving optimistic bilevel linear programs (BLPs) is to replace the lower-level problem with its Karush-Kuhn-Tucker (KKT) optimality conditions and reformulate the resulting complementarity constraints using auxiliary…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational…
It is well-known that proper scaling can increase the efficiency of computational problems. In this paper we define and show that a balancing technique can substantially improve the computational efficiency of optimal control algorithms. We…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…