Convex separable optimization is not much harder than linear optimization
Journal of the ACM (JACM)
Polynomial Methods for Separable Convex Optimization in Unimodular Linear Spaces with Applications
SIAM Journal on Computing
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
On Polyhedral Approximations of the Second-Order Cone
Mathematics of Operations Research
Convex Optimization
A Polynomial Time Algorithm for Computing an Arrow-Debreu Market Equilibrium for Linear Utilities
SIAM Journal on Computing
Market equilibrium via a primal--dual algorithm for a convex program
Journal of the ACM (JACM)
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Settling the Complexity of Arrow-Debreu Equilibria in Markets with Additively Separable Utilities
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the forty-second ACM symposium on Theory of computing
Spending Constraint Utilities with Applications to the Adwords Market
Mathematics of Operations Research
Rationality and Strongly Polynomial Solvability of Eisenberg-Gale Markets with Two Agents
SIAM Journal on Discrete Mathematics
Market equilibrium under separable, piecewise-linear, concave utilities
Journal of the ACM (JACM)
A Perfect Price Discrimination Market Model with Production, and a Rational Convex Program for It
Mathematics of Operations Research
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
| Hi-index | 0.00 |
We introduce the notion of a rational convex program (RCP) and we classify the known RCPs into two classes: quadratic and logarithmic. The importance of rationality is that it opens up the possibility of computing an optimal solution to the program via an algorithm that is either combinatorial or uses an LP-oracle. Next, we define a new Nash bargaining game, called ADNB, which is derived from the linear case of the Arrow-Debreu market model. We show that the convex program for ADNB is a logarithmic RCP, but unlike other known members of this class, it is nontotal. Our main result is a combinatorial, polynomial-time algorithm for ADNB. It turns out that the reason for infeasibility of logarithmic RCPs is quite different from that for LPs and quadratic RCPs. We believe that our ideas for surmounting the new difficulties will be useful for dealing with other nontotal RCPs as well. We give an application of our combinatorial algorithm for ADNB to an important “fair” throughput allocation problem on a wireless channel. Finally, we present a number of interesting questions that the new notion of RCP raises.