Properly optimal elements in vector optimization with variable ordering structures

In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Low-rank semidefinite programming for the MAX2SAT problem

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum satisfiability problems, but their application has traditionally been very limited by their speed and randomized nature. Our approach overcomes this difficult by using a recent approach to low-rank semidefinite programming, specialized to work in an incremental fashion suitable for use in an exact search algorithm. The method can be used both within complete or incomplete solver, and we demonstrate on a variety of problems from recent competitions. Our experiments show that the approach is faster (sometimes by orders of magnitude) than existing state-of-the-art complete and incomplete solvers, representing a substantial advance in search methods specialized for MAX2SAT problems.Comment: Accepted at AAAI'19. The code can be found at https://github.com/locuslab/mixsa

Expression Templates Revisited: A Performance Analysis of the Current ET Methodology

In the last decade, Expression Templates (ET) have gained a reputation as an efficient performance optimization tool for C++ codes. This reputation builds on several ET-based linear algebra frameworks focused on combining both elegant and high-performance C++ code. However, on closer examination the assumption that ETs are a performance optimization technique cannot be maintained. In this paper we demonstrate and explain the inability of current ET-based frameworks to deliver high performance for dense and sparse linear algebra operations, and introduce a new "smart" ET implementation that truly allows the combination of high performance code with the elegance and maintainability of a domain-specific language.Comment: 16 pages, 7 figure