Related papers: Warm-starting outer approximation for parametrized…
A key problem in multiobjective linear programming is to find the set of all efficient extreme points in objective space. In this paper we introduce oriented projective geometry as an efficient and effective framework for solving this…
The high computational complexity and energy consumption of artificial intelligence (AI) algorithms hinder their application in augmented reality (AR) systems. However, mobile edge computing (MEC) makes it possible to solve this problem.…
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…
Output thresholding is the technique to search for the best threshold to be used during inference for any classifiers that can produce probability estimates on train and testing datasets. It is particularly useful in high imbalance…
Optimization of Mixed-Integer Non-Linear Programming (MINLP) supports important decisions in applications such as Chemical Process Engineering. But current solvers have limited ability for deductive reasoning or the use of domain-specific…
Solving convex Semi-Infinite Programming (SIP) problems is challenging when the separation problem, i.e., the problem of finding the most violated constraint, is computationally hard. We propose to tackle this difficulty by solving the…
In this paper, we consider two types of problems that have some similarity in their structure, namely, min-min problems and min-max saddle-point problems. Our approach is based on considering the outer minimization problem as a minimization…
In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…
The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…
The XY-mixer has widespread utilization in modern quantum computing, including in variational quantum algorithms, such as Quantum Alternating Operator Ansatz (QAOA). The XY ansatz is particularly useful for solving Cardinality Constrained…
We present a linear cutting-plane relaxation approach that rapidly proves tight lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF). Our method leverages outer-envelope linear cuts for well-known second-order cone…
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…
This paper introduces scalable, sampling-based algorithms that optimize trained neural networks with ReLU activations. We first propose an iterative algorithm that takes advantage of the piecewise linear structure of ReLU neural networks…
This paper proposes an open-source distributed solver for solving Sparse Convex Optimization (SCO) problems over computational networks. Motivated by past algorithmic advances in mixed-integer optimization, the Sparse Convex Optimization…
This paper presents an improved mixed-integer model for the Thermal Unit Commitment Problem. By introducing new variables for the temperature of each thermal unit, the off-time-dependent start-up costs are modeled accurately and with a…
We generalize Farhi et al.'s 0.6924-approximation result technique of the Max-Cut Quantum Approximate Optimization Algorithm (QAOA) on 3-regular graphs to obtain provable lower bounds on the approximation ratio for warm-started QAOA. Given…
Nonconvex mixed-integer nonlinear programs (MINLPs) represent a challenging class of optimization problems that often arise in engineering and scientific applications. Because of nonconvexities, these programs are typically solved with…
The classic pump scheduling or Optimal Water Flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally…
Convex-concave min-max problems are ubiquitous in machine learning, and people usually utilize first-order methods (e.g., gradient descent ascent) to find the optimal solution. One feature which separates convex-concave min-max problems…
In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques…