Reduced RLT Representations for Nonconvex Polynomial Programming Problems

  • Evrim Dalkiran
  • Leo Liberti
  • Hanif D. Sherali
    • Categories Global Optimization Theory Tags , , , , ,

    This paper explores equivalent, reduced size Reformulation-Linearization Technique (RLT)-based formulations for polynomial programming problems. Utilizing a basis partitioning scheme for an embedded linear equality subsystem, we show that a strict subset of RLT defining equalities imply the remaining ones. Applying this result, we derive significantly reduced RLT representations and develop certain coherent associated branching rules … Read more

    Convex envelopes for quadratic and polynomial functions over polytopes

  • Marco Locatelli
    • Categories Global Optimization Theory Tags , , , ,

    In this paper we consider the problem of computing the value and a supporting hyperplane of the convex envelope for quadratic and polynomial functions over polytopes with known vertex set. We show that for general quadratic functions the computation can be carried on through a copositive problem, but in some cases (including all the two-dimensional … Read more

    Radio Planning of Energy-Aware Cellular Networks

  • Capone Antonio
  • Silvia Boiardi
  • Brunilde Sansò
    • Categories Telecommunications Tags , , , , ,

    The role of the Information and Communication Technology sector on productivity and economic growth is constantly increasing and, due to its pervasiveness, the ICT power consumption can no longer be ignored. Some energy-aware models and approaches have already been proposed for cellular networks, they aim at reducing power expenditures while decreasing network operators costs. However, … Read more

    Convergence analysis of primal-dual algorithms for total variation image restoration

  • Bingsheng He
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , , , , ,

    Recently, some attractive primal-dual algorithms have been proposed for solving a saddle-point problem, with particular applications in the area of total variation (TV) image restoration. This paper focuses on the convergence analysis of existing primal-dual algorithms and shows that the involved parameters of those primal-dual algorithms (including the step sizes) can be significantly enlarged if … Read more

    Symmetric tensor approximation hierarchies for the completely positive cone

  • Hongbo Dong
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    In this paper we construct two approximation hierarchies for the completely positive cone based on symmetric tensors. We show that one hierarchy corresponds to dual cones of a known polyhedral approximation hierarchy for the copositive cone, and the other hierarchy corresponds to dual cones of a known semidefinite approximation hierarchy for the copositive cone. As … Read more

    A modified DIRECT algorithm for a problem in astrophysics

  • Daniela di Serafino
  • Giampaolo Liuzzi
  • Veronica Piccialli
  • Gerardo Toraldo
  • Filippo Riccio
    • Categories Applications - Science and Engineering, Global Optimization Applications Tags , ,

    We present a modification of the DIRECT algorithm, called DIRECT-G, to solve a box-constrained global optimization problem arising in the detection of gravitational waves emitted by coalescing binary systems of compact objects. This is a hard problem since the objective function is highly nonlinear and expensive to evaluate, has a huge number of local extrema … Read more

    The Inexact Spectral Bundle Method for Convex Quadratic Semidefinite Programming

  • Huiling Lin
    • Categories Convex and Nonsmooth Optimization, Semi-definite Programming, Unconstrained Optimization Tags , ,

    We present an inexact spectral bundle method for solving convex quadratic semidefinite optimization problems. This method is a first-order method, hence requires much less computational cost each iteration than second-order approaches such as interior-point methods. In each iteration of our method, we solve an eigenvalue minimization problem inexactly, and solve a small convex quadratic semidefinite … Read more

    Estimating Derivatives of Noisy Simulations

  • Jorge Moré
  • Stefan M. Wild
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems, Other Topics Tags , ,

    We employ recent work on computational noise to obtain near-optimal finite difference estimates of the derivatives of a noisy function. Our analysis employs a stochastic model of the noise without assuming a specific form of distribution. We use this model to derive theoretical bounds for the errors in the difference estimates and obtain an easily … Read more

    Robust Unit Commitment Problem with Demand Response and Wind Energy

  • Bo Zeng
  • Long Zhao
    • Categories Robust Optimization, Scheduling Tags , , , ,

    To improve the efficiency in power generation and to reduce the greenhouse gas emission, both Demand Response (DR) strategy and intermittent renewable energy have been proposed or applied in electric power systems. However, the uncertainty and the generation pattern in wind farms and the complexity of demand side management pose huge challenges in power system … Read more

    Min-Max Theorems Related to Geometric Representations of Graphs and their SDPs

  • Marcel K. de Carli Silva
  • Levent Tunçel
    • Categories Combinatorial Optimization, Semi-definite Programming Tags , , ,

    Lovasz proved a nonlinear identity relating the theta number of a graph to its smallest radius hypersphere embedding where each edge has unit length. We use this identity and its generalizations to establish min-max theorems and to translate results related to one of the graph invariants above to the other. Classical concepts in tensegrity theory … Read more