Nonlinear programming: theory, algorithms, and applications
Nonlinear programming: theory, algorithms, and applications
Generalized linear multiplicative and fractional programming
Annals of Operations Research
SIAM Review
Global Optimization of 0-1 Hyperbolic Programs
Journal of Global Optimization
A Convex Envelope Formula for Multilinear Functions
Journal of Global Optimization
Semidefinite Programming Relaxation for NonconvexQuadratic Programs
Journal of Global Optimization
Journal of Global Optimization
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
Mathematical Programming: Series A and B
Computational Optimization and Applications
Journal of Global Optimization
A Global Optimization Method, QBB, for Twice-Differentiable Nonconvex Optimization Problem
Journal of Global Optimization
Improve-and-Branch Algorithm for the Global Optimization of Nonconvex NLP Problems
Journal of Global Optimization
Practical Global Optimization for Multiview Geometry
International Journal of Computer Vision
Journal of Global Optimization
Tight convex underestimators for $${{\mathcal C}^2}$$-continuous problems: I. univariate functions
Journal of Global Optimization
Triangulation of Points, Lines and Conics
Journal of Mathematical Imaging and Vision
A review of recent advances in global optimization
Journal of Global Optimization
Triangulation of points, lines and conics
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Globally Optimal Algorithms for Stratified Autocalibration
International Journal of Computer Vision
Projected Perspective Reformulations with Applications in Design Problems
Operations Research
Practical global optimization for multiview geometry
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Convex envelopes of products of convex and component-wise concave functions
Journal of Global Optimization
On interval-subgradient and no-good cuts
Operations Research Letters
A computational comparison of reformulations of the perspective relaxation: SOCP vs. cutting planes
Operations Research Letters
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In a recent work, we introduced the concept of convex extensions for lower semi-continuous functions and studied their properties. In this work, we present new techniques for constructing convex and concave envelopes of nonlinear functions using the theory of convex extensions. In particular, we develop the convex envelope and concave envelope of z=x/y over a hypercube. We show that the convex envelope is strictly tighter than previously known convex underestimators of x/y. We then propose a new relaxation technique for fractional programs which includes the derived envelopes. The resulting relaxation is shown to be a semidefinite program. Finally, we derive the convex envelope for a class of functions of the type f(x,y) over a hypercube under the assumption that f is concave in x and convex in y.