semidefinite

AI Hilbert: A New Paradigm for Scientific Discovery by Unifying Data and Background Knowledge

  • Ryan Cory-Wright
  • Bachir El Khadir
  • Cristina Cornelio
  • Sanjeeb Dash
  • Lior Horesh
    • Categories Basic Sciences Applications, Global Optimization Applications, Semi-definite Programming Tags , , ,

    The discovery of scientific formulae that parsimoniously explain natural phenomena and align with existing background theory is a key goal in science. Historically, scientists have derived natural laws by manipulating equations based on existing knowledge, forming new equations, and verifying them experimentally. In recent years, data-driven scientific discovery has emerged as a viable competitor in settings with … Read more

    CBLIB 2014: A benchmark library for conic mixed-integer and continuous optimization

  • Henrik A. Friberg
    • Categories Integer Programming, Linear, Cone and Semidefinite Programming, Optimization Software Benchmark Tags , , , , ,

    The Conic Benchmark Library (CBLIB 2014) is a collection of more than a hundred conic optimization instances under a free and open license policy. It is the first extensive benchmark library for the advancing field of conic mixed-integer and continuous optimization, which is already supported by all major commercial solvers and spans a wide range … Read more

    Strong Duality and Minimal Representations for Cone Optimization

  • Levent Tunçel
  • Henry Wolkowicz
    • Categories Convex Optimization, Semi-definite Programming Tags , , ,

    The elegant results for strong duality and strict complementarity for linear programming, \LP, can fail for cone programming over nonpolyhedral cones. One can have: unattained optimal values; nonzero duality gaps; and no primal-dual optimal pair that satisfies strict complementarity. This failure is tied to the nonclosure of sums of nonpolyhedral closed cones. We take a … Read more

    On Extracting Maximum Stable Sets in Perfect Graphs Using Lovasz’s Theta Function

  • Xiaofei Fan
  • E. Alper Yildirim
    • Categories Combinatorial Optimization, Semi-definite Programming Tags , ,

    We study the maximum stable set problem. For a given graph, we establish several transformations among feasible solutions of different formulations of Lov{\’a}sz’s theta function. We propose reductions from feasible solutions corresponding to a graph to those corresponding to its subgraphs. We develop an efficient, polynomial-time algorithm to extract a maximum stable set in a … Read more