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Michael Corral

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Optimization is the science of making a best choice in the face of conflicting requirements. Any convex optimization problem has geometric interpretation. If a given optimization problem can be transformed to a convex equivalent, then this interpretive benefit is acquired. That is a powerful attraction: the ability to visualize geometry of an optimization problem. Conversely, recent advances in geometry hold convex optimization within their proofs' core. This book is about convex optimization, convex geometry (with particular attention to distance geometry), geometrical problems, and problems that can be transformed into geometrical problems. Euclidean distance geometry is, fundamentally, a determination of point conformation from interpoint distance information; e.g., given only distance information, determine whether there corresponds a realizable configuration of points; a list of points in some dimension that attains the given interpoint distances., Expert information on convex optimization expert calculus of inequalities

This series of video lectures and lecture notes features the theory of convex analysis in finite dimensions and applications to optimization. The lectures are based on my recently published book “An Easy Path to Convex Analysis and Applications”  (co-authored with Boris Mordukhovich) published by the Morgan & Claypool in 2013.  Important topics of convex analysis such as subgradients, subdifferential calculus…

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This site introduces the first of two printed volumes exploring the algebraic work of Hermann Grassmann as it re-emerges from one and a half centuries of isolation.

Full course preparation material, teaching guides, all subjects, all levels: K12, College, continuing ed. Complete Teacher Prep Materials, full course lesson plans, aids, cirriculum guides, syllabus.