相关论文: Bounds and convex heuristics for bi-objective opti…
Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best solution in this set is in general a challenging task: In the case of three or more objectives…
Many real-world optimisation problems involve multiple objectives. When considered concurrently, they give rise to a set of optimal trade-off solutions, also known as efficient solutions. These solutions have the property that neither…
This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…
Scalarization allows to solve a multi-objective optimization problem by solving many single-objective sub-problems, uniquely determined by some parameters. In this work, we propose several adaptive strategies to select such parameters in…
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…
We consider a class of convex optimization problems over the simplex of probability measures. Our framework comprises optimal experimental design (OED) problems, in which the measure over the design space indicates which experiments are…
Experimental design is central to science and engineering. A ubiquitous challenge is how to maximize the value of information obtained from expensive or constrained experimental settings. Bayesian optimal experimental design (OED) provides…
We address high-dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications.…
Real-world problems are often multi-objective with decision-makers unable to specify a priori which trade-off between the conflicting objectives is preferable. Intuitively, building machine learning solutions in such cases would entail…
We present a multi-objective Bayesian optimisation algorithm that allows the user to express preference-order constraints on the objectives of the type "objective A is more important than objective B". These preferences are defined based on…
Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the…
Optimizing nonlinear systems involving expensive computer experiments with regard to conflicting objectives is a common challenge. When the number of experiments is severely restricted and/or when the number of objectives increases,…
In this paper we analyze theoretical properties of bi-objective convex-quadratic problems. We give a complete description of their Pareto set and prove the convexity of their Pareto front. We show that the Pareto set is a line segment when…
According to the fundamental theorems of welfare economics, any competitive equilibrium is Pareto efficient. Unfortunately, competitive equilibrium prices only exist under strong assumptions such as perfectly divisible goods and convex…
In multiobjective optimization, most branch and bound algorithms provide the decision maker with the whole Pareto front, and then decision maker could select a single solution finally. However, if the number of objectives is large, the…
In this work, we propose a novel method to tackle the problem of multiobjective optimization under parameteric uncertainties, by considering the Conditional Pareto Sets and Conditional Pareto Fronts. Based on those quantities we can define…
Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the…