Convexity and Optimization in Finite Dimensions I

TL;DR: In this article, the authors give necessary and sufficient conditions for a cone to be the orthogonal transform of the positive orthant, and show that if K is a cone which is contained in its dual, then there is a self-dual cone containing K.

TL;DR: The determinate allocation decision model and the probabilistic allocation decisionmodel of a kind of renewable resource are separately studied by means of dynamic programming, and the optimal allocation policy is given under some special conditions.

TL;DR: If the authors connect ideal transformers and conical diodes resulting in a 'transformer diode multiport' (TD-multiport) the permissible voltage vectors and current vectors at the exposed ports form complementary polar cones, then the voltage vector appearing across the ports of the multiport would be the projection of the voltage source vector E onto the port voltage cone of the Multiport.

TL;DR: This work provides a single-letter characterization of the maximin game of the random coding error exponent associated with the average probability of erroneously decoding the watermark in the case where the covertext source is memoryless.