Related papers: Fully piecewise linear vector optimization problem
We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…
It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this…
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…
In this paper, we are dealing with constrained vector optimisation problems where the objective function acts between real linear-topological spaces. Our aim is to study the relationships between the sets of properly efficient solutions to…
According to the published papers and books since the turn of the century, Pareto optimization is the dominating assessment method for multi-objective nonlinear optimization problems treated by population-based optimizers like Evolutionary…
Efficiently solving multi-objective optimization problems for simulation optimization of important scientific and engineering applications such as materials design is becoming an increasingly important research topic. This is due largely to…
This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…
Many real-world decision-making problems involve optimizing multiple objectives simultaneously, rendering the selection of the most preferred solution a non-trivial problem: All Pareto optimal solutions are viable candidates, and it is…
We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction of MIP formulations to derive new formulations for…
We study a broad class of polynomial optimization problems whose constraints and objective functions exhibit sparsity patterns. We give two characterizations of the number of critical points to these problems, one as a mixed volume and one…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…
Parametric optimization solves a family of optimization problems as a function of parameters. It is a critical component in situations where optimal decision making is repeatedly performed for updated parameter values, but computation…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…
Linear programming on the Stiefel manifold (LPS) is studied for the first time. It aims at minimizing a linear objective function over the set of all $p$-tuples of orthonormal vectors in ${\mathbb R}^n$ satisfying $k$ additional linear…
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is…
We convert, within polynomial-time and sequential processing, an NP-Complete Problem into a real-variable problem of minimizing a sum of Rational Linear Functions constrained by an Asymptotic-Linear-Program. The coefficients and constants…
Multi-objective probabilistic model checking provides a way to verify several, possibly conflicting, quantitative properties of a stochastic system. It has useful applications in controller synthesis and compositional probabilistic…
We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for obtaining dual bounds at a node, for checking node fathoming,…
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…