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Author Lasserre, Jean B.
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Inverse Polynomial Optimization ♦ Semidefinite Program ♦ Polynomial Program Min ♦ Explicit Canonical Form ♦ Systematic Numerical Scheme ♦ Putinar Certificate ♦ Current Feasible Solution ♦ Global Minimizer ♦ Fd Reduces ♦ Priori Degree ♦ Optimal Value ♦ Inverse Optimization Problem ♦ Inverse Optimal Solution ♦ Unknown Optimal Value
Abstract Abstract. We consider the inverse optimization problem associated with the polynomial program f ∗ = min{f(x) : x ∈ K} and a given current feasible solution y ∈ K. We provide a systematic numerical scheme to compute an inverse optimal solution. That is, we compute a polynomial ˜ f (which may be of same degree as f if desired) with the following properties: (a) y is a global minimizer of ˜ f on K with a Putinar’s certificate with an a priori degree bound d fixed, and (b), ˜ f minimizes ‖f − ˜ f ‖ (which can be the ℓ1, ℓ2 or ℓ∞-norm of the coefficients) over all polynomials with such properties. Computing ˜ fd reduces to solving a semidefinite program whose optimal value also provides a bound on how far is f(y) from the unknown optimal value f ∗. The size of the semidefinite program can be adapted to to computational capabilities available. Moreover, if one uses the ℓ1-norm, then ˜ f takes a simple and explicit canonical form. Some variations are also discussed. 1.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article