Strict efficiency in set optimization studied with the set approach

This paper is devoted to strict efficiency in set optimization studied with the set approach. Strict efficient solutions are defined with respect to the $l$-type less order relation and the possibly less order relation. Scalar characterization and necessary and/or sufficient conditions for such solutions are obtained. In particular, we establish some conditions expressed in terms … Read more

On Necessary Optimality Conditions for Sets of Points in Multiobjective Optimization

Taking inspiration from what is commonly done in single-objective optimization, most local algorithms proposed for multiobjective optimization extend the classical iterative scalar methods and produce sequences of points able to converge to single efficient points. Recently, a growing number of local algorithms that build sequences of sets has been devised, following the real nature of … Read more

On the accurate detection of the Pareto frontier for bi-objective mixed integer linear problems

We propose a criterion space search algorithm for bi-objective mixed integer linear programming problems. The Pareto frontier of these problems can have a complex structure, as it can include isolated points, open, half-open and closed line segments. Therefore, its exact detection is an achievable though hard computational task. Our algorithm works by alternating the resolution … Read more

Considering homeowner acceptance of retrofit measures within energy supply network optimization

A key factor towards a low-carbon society is energy efficient heating of private houses. The choice of heating technology as well as the decision for certain energy-efficient house renovations are made mainly by individual homeowners. In contrast, municipal energy network planning heavily depends on and strongly affects these decisions. Further, there are different conflicting objectives … Read more

A Subspace Minimization Barzilai-Borwein Method for Multiobjective Optimization Problems

Nonlinear conjugate gradient methods have recently garnered significant attention within the multiobjective optimization community. These methods aim to maintain consistency in conjugate parameters with their single-objective optimization counterparts. However, the preservation of the attractive conjugate property of search directions remains uncertain, even for quadratic cases, in multiobjective conjugate gradient methods. This loss of interpretability of … Read more

Preconditioned Barzilai-Borwein Methods for Multiobjective Optimization Problems

Preconditioning is a powerful approach for solving ill-conditioned problems in optimization, where a preconditioning matrix is used to reduce the condition number and speed up the convergence of first-order method. Unfortunately, it is impossible to capture the curvature of all objective functions with a single preconditioning matrix in multiobjective optimization. Instead, second-order methods for multiobjective … Read more

Second-Order Strong Optimality and Second-Order Duality for Nonsmooth Constrained Multiobjective Fractional Programming Problems

\(\) This paper investigates constrained nonsmooth multiobjective fractional programming problem (NMFP) in real Banach spaces. It derives a quotient calculus rule for computing the first- and second-order Clarke derivatives of fractional functions involving locally Lipschitz functions. A novel second-order Abadie-type regularity condition is presented, defined with the help of the Clarke directional derivative and the … Read more

Uncertainty Quantification for Multiobjective Stochastic Convex Quadratic Programs

A multiobjective stochastic convex quadratic program (MOSCQP) is a multiobjective optimization problem with convex quadratic objectives that are observed with stochastic error. MOSCQP is a useful problem formulation arising, for example, in model calibration and nonlinear system identification when a single regression model combines data from multiple distinct sources, resulting in a multiobjective least squares … Read more

The convergence rate of the Sandwiching algorithm for convex bounded multiobjective optimization

Sandwiching algorithms, also known as Benson-type algorithms, approximate the nondominated set of convex bounded multiobjective optimization problems by constructing and iteratively improving polyhedral inner and outer approximations. Using a set-valued metric, an estimate of the approximation quality is determined as the distance between the inner and outer approximation. The convergence of the algorithm is evaluated … Read more

Computing an approximation of the nondominated set of multi-objective mixed-integer nonlinear optimization problems

In practical applications, one often has not only one, but several objectives that need to be optimized simultaneously. What is more, modeling such real world problems usually involves using both, continuous and integer variables. This then results in multi-objective mixed-integer optimization problems, which are in focus of this paper. We present an approximation concept, called … Read more