Many combinatorial optimization problems have underlying goal functions that are submodular. The classical goal is to find a good solution for a given submodular function f under a given set of constraints. In this paper, we investigate the runtime of a multi-objective evolutionary algorithm called GSEMO until it has obtained a good approximation for submodular functions. For the case of monoto...

Continuing the work of Hiriart-Urruty and Phelps, we discuss (in both locally convex spaces and Banach spaces) the formulas for the conjugates and subdifferentials of the precomposition of a convex function by a continuous linear mapping and the marginal function of a convex function by a continuous linear mapping. We exhibit a certain (incomplete) duality between the operations of precompositi...

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, MAXIMUM ACYCLIC SUBGRAPH and MAXIMUM BETWEENNESS, we prove NP-hard approximation factors of 14 15 + ε and 1 2 + ε . When it is hard to approximate an OCSP by a constant better than taking a uniformly-at-random ordering, then the OCSP is said to be approximation r...

A highly competitive micro evolutionary algorithm to solve unconstrained optimization problems called μJADE (micro adaptive differential evolution), is adapted to deal with constrained search spaces. Two constraint-handling techniques (the feasibility rules and the ε-constrained method) are tested in μJADE and their performance is analyzed. The most competitive version is then compared against ...

This work is concerned with approximating constraint satisfaction problems (CSPs) with an additional global cardinality constraints. For example, Max Cut is a boolean CSP where the input is a graph G = (V, E) and the goal is to find a cut S ∪ S̄ = V that maximizes the number of crossing edges, |E(S , S̄ )|. The Max Bisection problem is a variant of Max Cut with an additional global constraint tha...

Abstract. To deal with the divergence-free constraint in a double curl problem: curlμ−1curlu = f and div εu = 0 in Ω, where μ and ε represent the physical properties of the materials occupying Ω, we develop a δ-regularization method: curlμcurluδ + δεuδ = f to completely ignore the divergence-free constraint div εu = 0. It is shown that uδ converges to u in H(curl ; Ω) norm as δ → 0. The edge fi...