Related papers: A multi-criteria approach to approximate solution …
The structure of many real-world optimization problems includes minimization of a nonlinear (or quadratic) functional subject to bound and singly linear constraints (in the form of either equality or bilateral inequality) which are commonly…
We propose a new methodology for parameterized constrained robust optimization, an important class of optimization problems under uncertainty, based on learning with a self-supervised penalty-based loss function. Whereas supervised learning…
This paper considers the stochastic convex composite optimization problem and presents multi-cut stochastic approximation (SA) methods for solving it, whose models in expectation overestimate its objective function. The multi-cut model…
We consider a decision-making problem to find absolute ratings of alternatives that are compared in pairs under multiple criteria, subject to constraints in the form of two-sided bounds on ratios between the ratings. Given matrices of…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the…
Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…
We determine the power of the weighted sum scalarization with respect to the computation of approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion of…
We study the problem of maximizing a monotone increasing submodular function over a set of weighted elements subject to a knapsack constraint. Although this problem is NP-hard, many applications require exact solutions, as approximate…
In this paper, we study the problem of maximizing $k$-submodular functions subject to a knapsack constraint. For monotone objective functions, we present a $\frac{1}{2}(1-e^{-2})\approx 0.432$ greedy approximation algorithm. For the…
Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern day…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
We study the knapsack problem with group fairness constraints. The input of the problem consists of a knapsack of bounded capacity and a set of items, each item belongs to a particular category and has and associated weight and value. The…
We study the approximation of general multiobjective optimization problems with the help of scalarizations. Existing results state that multiobjective minimization problems can be approximated well by norm-based scalarizations. However, for…
An important goal in algorithm design is determining the best running time for solving a problem (approximately). For some problems, we know the optimal running time, assuming certain conditional lower bounds. In this work, we study the…
The balance between convergence and diversity is a key issue of evolutionary multi-objective optimization. The recently proposed stable matching-based selection provides a new perspective to handle this balance under the framework of…
In this paper, a new upper bound for the Multiple Knapsack Problem (MKP) is proposed, based on the idea of relaxing MKP to a {\em Bounded Sequential Multiple Knapsack Problem}, i.e., a multiple knapsack problem in which item sizes are…
We study the correlated stochastic knapsack problem of a submodular target function, with optional additional constraints. We utilize the multilinear extension of submodular function, and bundle it with an adaptation of the relaxed linear…
We propose a novel approach to solve K-adaptability problems with convex objective and constraints and integer first-stage decisions. A logic-based Benders decomposition is applied to handle the first-stage decisions in a master problem,…